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1 · Current

Reading text: Noto Serif · Labels, tables, small text: Noto Sans · Formulas and calculations: Courier Prime

Approach

The target is fixed: Rs 2,500,000 must be in the fund at the end of Year 15. The fund earns 9% a year. In each part we ask the same question: what deposit grows to Rs 2,500,000 by Year 15? Only the timing of the deposits changes, so only the factor changes.

Part i equal deposits at the end of each year. This is an ordinary annuity, so we divide by FVIFA.
Part ii one deposit at the end of the first year. It earns interest for 14 years only, so we use a single-sum factor for 14 years.
Part iii equal deposits at the beginning of each year. This is an annuity due, so we divide by .

Terms used

FVIF (future value interest factor): The amount Re 1 grows to after n years at rate i. Here , so Re 1 today becomes Rs 3.642 in 15 years.

FVIFA (future value interest factor of an annuity): The amount that Re 1 deposited at the END of every year grows to after n years. Here , so 15 deposits of Re 1 become Rs 29.361.

Ordinary annuity and annuity due: An ordinary annuity pays at the end of each period. An annuity due pays at the beginning of each period, so every payment earns one extra year of interest.

Future value: Rs 2,500,000 needed at the end of Year 15
FVIFA(n, i): 29.361 for n = 15 years and i = 9% (given)

Working

Part i annual payment at the end of each year

Write the relation
15 equal year-end deposits must accumulate to the target; FVIFA is given in the question.
Solve for the payment
=Rs 85,146.96 per year
Deposits are made at the end of Year 1 to Year 15.

Time graph

Part i 15 year-end deposits compounded at 9% to Year 15

Year	Cash flow	Amount	Compound factor	Future value
1–15	Deposit at the end of each year	85,146.96	29.361	2,499,999.89
Fund at end of Year 15 (Rs 2,500,000 after rounding)				2,499,999.89

2 · Noto Serif + Inter

Reading text: Noto Serif · Labels, tables, small text: Inter · Formulas and calculations: JetBrains Mono

Approach

The target is fixed: Rs 2,500,000 must be in the fund at the end of Year 15. The fund earns 9% a year. In each part we ask the same question: what deposit grows to Rs 2,500,000 by Year 15? Only the timing of the deposits changes, so only the factor changes.

Part i equal deposits at the end of each year. This is an ordinary annuity, so we divide by FVIFA.
Part ii one deposit at the end of the first year. It earns interest for 14 years only, so we use a single-sum factor for 14 years.
Part iii equal deposits at the beginning of each year. This is an annuity due, so we divide by .

Terms used

FVIF (future value interest factor): The amount Re 1 grows to after n years at rate i. Here , so Re 1 today becomes Rs 3.642 in 15 years.

FVIFA (future value interest factor of an annuity): The amount that Re 1 deposited at the END of every year grows to after n years. Here , so 15 deposits of Re 1 become Rs 29.361.

Ordinary annuity and annuity due: An ordinary annuity pays at the end of each period. An annuity due pays at the beginning of each period, so every payment earns one extra year of interest.

Future value: Rs 2,500,000 needed at the end of Year 15
FVIFA(n, i): 29.361 for n = 15 years and i = 9% (given)

Working

Part i annual payment at the end of each year

Write the relation
15 equal year-end deposits must accumulate to the target; FVIFA is given in the question.
Solve for the payment
=Rs 85,146.96 per year
Deposits are made at the end of Year 1 to Year 15.

Time graph

Part i 15 year-end deposits compounded at 9% to Year 15

Year	Cash flow	Amount	Compound factor	Future value
1–15	Deposit at the end of each year	85,146.96	29.361	2,499,999.89
Fund at end of Year 15 (Rs 2,500,000 after rounding)				2,499,999.89

3 · Source Serif + Source Sans

Reading text: Source Serif 4 · Labels, tables, small text: Source Sans 3 · Formulas and calculations: Courier Prime

Approach

The target is fixed: Rs 2,500,000 must be in the fund at the end of Year 15. The fund earns 9% a year. In each part we ask the same question: what deposit grows to Rs 2,500,000 by Year 15? Only the timing of the deposits changes, so only the factor changes.

Part i equal deposits at the end of each year. This is an ordinary annuity, so we divide by FVIFA.
Part ii one deposit at the end of the first year. It earns interest for 14 years only, so we use a single-sum factor for 14 years.
Part iii equal deposits at the beginning of each year. This is an annuity due, so we divide by .

Terms used

FVIF (future value interest factor): The amount Re 1 grows to after n years at rate i. Here , so Re 1 today becomes Rs 3.642 in 15 years.

FVIFA (future value interest factor of an annuity): The amount that Re 1 deposited at the END of every year grows to after n years. Here , so 15 deposits of Re 1 become Rs 29.361.

Ordinary annuity and annuity due: An ordinary annuity pays at the end of each period. An annuity due pays at the beginning of each period, so every payment earns one extra year of interest.

Future value: Rs 2,500,000 needed at the end of Year 15
FVIFA(n, i): 29.361 for n = 15 years and i = 9% (given)

Working

Part i annual payment at the end of each year

Write the relation
15 equal year-end deposits must accumulate to the target; FVIFA is given in the question.
Solve for the payment
=Rs 85,146.96 per year
Deposits are made at the end of Year 1 to Year 15.

Time graph

Part i 15 year-end deposits compounded at 9% to Year 15

Year	Cash flow	Amount	Compound factor	Future value
1–15	Deposit at the end of each year	85,146.96	29.361	2,499,999.89
Fund at end of Year 15 (Rs 2,500,000 after rounding)				2,499,999.89

4 · Literata + Figtree (chosen)

Reading text: Literata · Labels, tables, small text: Figtree · Formulas and calculations: IBM Plex Mono

Approach

The target is fixed: Rs 2,500,000 must be in the fund at the end of Year 15. The fund earns 9% a year. In each part we ask the same question: what deposit grows to Rs 2,500,000 by Year 15? Only the timing of the deposits changes, so only the factor changes.

Part i equal deposits at the end of each year. This is an ordinary annuity, so we divide by FVIFA.
Part ii one deposit at the end of the first year. It earns interest for 14 years only, so we use a single-sum factor for 14 years.
Part iii equal deposits at the beginning of each year. This is an annuity due, so we divide by .

Terms used

FVIF (future value interest factor): The amount Re 1 grows to after n years at rate i. Here , so Re 1 today becomes Rs 3.642 in 15 years.

FVIFA (future value interest factor of an annuity): The amount that Re 1 deposited at the END of every year grows to after n years. Here , so 15 deposits of Re 1 become Rs 29.361.

Ordinary annuity and annuity due: An ordinary annuity pays at the end of each period. An annuity due pays at the beginning of each period, so every payment earns one extra year of interest.

Future value: Rs 2,500,000 needed at the end of Year 15
FVIFA(n, i): 29.361 for n = 15 years and i = 9% (given)

Working

Part i annual payment at the end of each year

Write the relation
15 equal year-end deposits must accumulate to the target; FVIFA is given in the question.
Solve for the payment
=Rs 85,146.96 per year
Deposits are made at the end of Year 1 to Year 15.

Time graph

Part i 15 year-end deposits compounded at 9% to Year 15

Year	Cash flow	Amount	Compound factor	Future value
1–15	Deposit at the end of each year	85,146.96	29.361	2,499,999.89
Fund at end of Year 15 (Rs 2,500,000 after rounding)				2,499,999.89

5 · IBM Plex throughout

Reading text: IBM Plex Serif · Labels, tables, small text: IBM Plex Sans · Formulas and calculations: IBM Plex Mono

Approach

The target is fixed: Rs 2,500,000 must be in the fund at the end of Year 15. The fund earns 9% a year. In each part we ask the same question: what deposit grows to Rs 2,500,000 by Year 15? Only the timing of the deposits changes, so only the factor changes.

Part i equal deposits at the end of each year. This is an ordinary annuity, so we divide by FVIFA.
Part ii one deposit at the end of the first year. It earns interest for 14 years only, so we use a single-sum factor for 14 years.
Part iii equal deposits at the beginning of each year. This is an annuity due, so we divide by .

Terms used

FVIF (future value interest factor): The amount Re 1 grows to after n years at rate i. Here , so Re 1 today becomes Rs 3.642 in 15 years.

FVIFA (future value interest factor of an annuity): The amount that Re 1 deposited at the END of every year grows to after n years. Here , so 15 deposits of Re 1 become Rs 29.361.

Ordinary annuity and annuity due: An ordinary annuity pays at the end of each period. An annuity due pays at the beginning of each period, so every payment earns one extra year of interest.

Future value: Rs 2,500,000 needed at the end of Year 15
FVIFA(n, i): 29.361 for n = 15 years and i = 9% (given)

Working

Part i annual payment at the end of each year

Write the relation
15 equal year-end deposits must accumulate to the target; FVIFA is given in the question.
Solve for the payment
=Rs 85,146.96 per year
Deposits are made at the end of Year 1 to Year 15.

Time graph

Part i 15 year-end deposits compounded at 9% to Year 15

Year	Cash flow	Amount	Compound factor	Future value
1–15	Deposit at the end of each year	85,146.96	29.361	2,499,999.89
Fund at end of Year 15 (Rs 2,500,000 after rounding)				2,499,999.89

6 · One serif for everything

Reading text: Noto Serif · Labels, tables, small text: Noto Serif · Formulas and calculations: Courier Prime

Approach

The target is fixed: Rs 2,500,000 must be in the fund at the end of Year 15. The fund earns 9% a year. In each part we ask the same question: what deposit grows to Rs 2,500,000 by Year 15? Only the timing of the deposits changes, so only the factor changes.

Part i equal deposits at the end of each year. This is an ordinary annuity, so we divide by FVIFA.
Part ii one deposit at the end of the first year. It earns interest for 14 years only, so we use a single-sum factor for 14 years.
Part iii equal deposits at the beginning of each year. This is an annuity due, so we divide by .

Terms used

FVIF (future value interest factor): The amount Re 1 grows to after n years at rate i. Here , so Re 1 today becomes Rs 3.642 in 15 years.

FVIFA (future value interest factor of an annuity): The amount that Re 1 deposited at the END of every year grows to after n years. Here , so 15 deposits of Re 1 become Rs 29.361.

Ordinary annuity and annuity due: An ordinary annuity pays at the end of each period. An annuity due pays at the beginning of each period, so every payment earns one extra year of interest.

Future value: Rs 2,500,000 needed at the end of Year 15
FVIFA(n, i): 29.361 for n = 15 years and i = 9% (given)

Working

Part i annual payment at the end of each year

Write the relation
15 equal year-end deposits must accumulate to the target; FVIFA is given in the question.
Solve for the payment
=Rs 85,146.96 per year
Deposits are made at the end of Year 1 to Year 15.

Time graph

Part i 15 year-end deposits compounded at 9% to Year 15

Year	Cash flow	Amount	Compound factor	Future value
1–15	Deposit at the end of each year	85,146.96	29.361	2,499,999.89
Fund at end of Year 15 (Rs 2,500,000 after rounding)				2,499,999.89