Deshaun needs 18464 for a future project. He can invest 4000 now at an annual rate of 8% , compounded semiannually. Assuming that no withdrawals are made, how long will it take for him to have enough money for his project?

Solution

Des ha u n n ee d s 18464 f or a f u t u re p ro j ec t . He c an in v es t 4000 n o w a t an ann u a l r a t e o f 8%, co m p o u n d e d se miann u a ll y . A ss u min g t ha t n o w i t h d r a w a l s a re ma d e, h o w l o n g w i ll i t t ak e f or him t o ha v e e n o ug h m o n ey f or hi s p ro j ec t ?

Time : 19.5

Solution steps

Translate the problem into an equation:

18464 = 4000 (1 + \frac{0.08}{2})^{2 t}

Solve for

t, 18464 = 4000 (1 + \frac{0.08}{2})^{2 t} : t = 19.5

Time : 19.5