Question

Stewart is saving for a holiday. He deposits a fixed amount every quarter in a bank account with an EAR of 15%. If this account pays interest every month then how much should he save from each quarterly paycheck in order to have $20,000 in the account in four years' time? Show work

Select one:

a. 861.38

b. 1,143.79

c. 949.47

d. 934.90

Answer 1

c. 949.47

Note: Intermediate calculations are not rounded off.

Step-1:Calculation of Annual percentage rate and then quarterly interest rate

Where,

((1+(i/n))^n)-1

=

E

i

Annual percentage rate

?

((1+(i/4))^4)-1

=

0.15

n

number of times compounding in a year

4

(1+(i/4))^4

1.15

E

Effective annual interest rate

15%

1+(i/4)

1.035558

i/4

0.035558

i

14.22%

So,

Annual percentage rate

14.22%

And Quarterly interest rate

3.56%

Step-2:Calculation of quarterly deposit

Quarterly deposit

=

Future Value of quarterly deposit/Future value of annuity of 1

=

$ 20,000.00

/

21.06431

=

$       949.47

Working;

Future Value of annuity of 1

=

(((1+i)^n)-1)/i

Where,

=

(((1+0.0356)^16)-1)/0.0356

i

3.56%

=

21.0643074

n

16