Question

Chaim has won $5,000 and wants to save it towards buying a house in six years when he finishes his law degree. He has the choice between an account which compounds daily (so n=365) with an APR of 7% and another which also has a 7% APR but compounds quarterly (so n=4). How much more interest will he earn if he chooses the first account? Chaim will earn $________ more by choosing the first account. (Enter an answer rounded to two decimal places.)

Answer 1

Chaim will earn $3.21 more by choosing the first account.

Explanation:

We find the Future value of the accounts

Future value formula = Present value × (1 + r/n)ⁿ

Where r = rate

n = compounding frequency

For Account 1

Compounds daily (so n=365) with an APR of 7%

Future value

= 5000 × (1 + 0.07/365)³⁶⁵

= 5000 × (1 + 0.0001917808)³⁶⁵

= $5362.504873

Interest = Future value - Present value = $(5362.504873 - 5000)

= $362.504873

Account 2

7% APR but compounds quarterly (so n=4).

Future value = 5000 × (1 + 0.07/4)⁴

= 5000 × (1 + 0.0175)⁴

= $5359.2951564

Interest = Future value - Present value

= $(5359.2951564 - 5000)

= $359.2951564

How much more interest will he earn if he chooses the first account?

Interest (first account) - Interest (second account)

= $362.504873 - $359.2951564

= $3.2097166

Approximately to 2 decimal places

= $3.21

Chaim will earn $3.21 more by choosing the first account.