First City Bank pays 8 percent simple interest on its savings account balances, whereas Second City Bank pays 8 percent interest compounded annually.

First City Bank pays 8 percent simple interest on its savings account balances, whereas Second City Bank pays 8 percent interest compounded annually.

  

If you made a $65,000 deposit in each bank, how much more money would you earn from your Second City Bank account at the end of 8 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

Difference in accounts

$

 

Explanation:

The time line for the cash flows is:

   

0		8
$65,000		FV

The simple interest per year is:

$65,000 × .08 = $5,200

So after 8 years you will have:

$5,200 × 8 = $41,600 in interest.

The total balance will be $65,000 + 41,600 = $106,600

With compound interest we use the future value formula:

FV = PV(1 + r)t

FV = $65,000(1.08)8 = $120,310.46

The difference is:

$120,310.46 – 106,600 = $13,710.46

Calculator Solution:

 

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

 

Enter

8

8%

±$65,000

N

I/Y

PV

PMT

FV

Solve for

$120,310.46

$120,310.46 − 106,600 = $13,710.46