Question

Sam got a job at the Brick. He plans to save $500 every month for 3 years to buy a car. The savings account earns 2.25% compounded semi-annually. If he puts the money in his savings account at the beginning of each month, what will be the balance in the account at the end of the three-year term?

Select one:

A. $18 603.37

B. $18 638.25

C. $17 390.19

D. $18 635.22

E. $18 600.50

Answer 1

(1 + APR/n)^n = (1 + APR/n)^n

(1 + 0.0225/2)^2 = (1 + APR/12)^12

(1 + 0.01125)^2 = (1 + APR/12)^12

1.022627 = (1 + APR/12)^12

1.001866 = 1 + APR/12

0.001866 = APR/12

APR = 0.02239525 or 2.239525%

Monthly rate = 2.239525% / 12 = 0.186627

Future value = (1 + r) * Payments * [(1 + r)^n - 1] / r

Future value = (1 + 0.00186627) * 500 * [(1 +0.00186627 )^36 - 1] / 0.00186627

Future value = 1.00186627 * 500 [1.069427 - 1] / 0.00186627

Future value = 1.00186627 * 500 * 37.20106

Future value = $18,635.22