Question

Ethan wants to set aside a sum of $5,000 to start his ‘holiday’ savings account. Which of the following options will give him the highest value in 6 years? Assume an interest rate of 3%

• Invest $5,000 as a lump sum today
• Invest a lump sum of $5,000 today and $1,000 and another $1,000 at the end of the year for the next five years ie $5,000 plus 5 amounts of $1,000 annually.
• Invest $1,200 at the end of years 1, 3 and 5

Answer 1

Option-1)

Lumpsum invested today = $ 5000

Future value = Invested Today(1+Interest Rate)^n

= 5000(1+0.03)^6

Future Value in 6 years = $ 5970.26

Option-2)

Future value of $ 5000 invested is $ 5970.26 (as computed above)

Calculating the Future value at the end of 5 years of periodic deposit of $ 1000 each year for 5 years:-

Where, C= Periodic Deposits = $1000

r = Periodic Interest rate = 0.03

n= no of periods = 5

Future value at the end of 5 years is $ 5309.14

These deposits will earn interest for another year.

Future value of periodic deposit at year end 6 = 5309.14(1+0.03)

= $ 5468.41

So, total Future value = $ 5970.26 + $5468.41

= $ 11,438.67

Option-3)

Invested $1,200 at the end of years 1, 3 and 5

Future Value = 1200(1+0.03)^5 + 1200(1+0.03)^3 + 1200(1+0.03)^1

= 1391.13 + 1311.27 + 1236

= $ 3938.4

So, Option-2 will give highest value in 6 years.

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