First City Bank pays 6 percent simple interest on its savings account balances, whereas Second City Bank pays 6 percent interest compounded annually.

First City Bank pays 6 percent simple interest on its savings account balances, whereas Second City Bank pays 6 percent interest compounded annually.
If you made a $72,000 deposit in each bank, how much more money would you earn from your Second City Bank account at the end of 10 years?

Answer




Explanation

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

The time line for the cash flows is:

   

0		10
$72,000		FV

The simple interest per year is:

$72,000 × .06 = $4,320

So after 10 years you will have:

$4,320 × 10 = $43,200 in interest.

The total balance will be $72,000 + 43,200 = $115,200

With compound interest we use the future value formula:

FV = PV(1 + r)t

FV = $72,000(1.06)10 = $128,941.03

The difference is:

$128,941.03 – 115,200 = $13,741.03

Calculator Solution:

 

Enter

10

6%

±$72,000

N

I/Y

PV

PMT

FV

Solve for

$128,941.03

$128,941.03 − 115,200 = $13,741.03