Samuel invested 8,400 in an account paying an interest rate of 6.4% compounded quarterly. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach 21,090?

Solution

S am u e l in v es t e d 8, 400 in an a cco u n t p a y in g an in t eres t r a t e o f 6.4% co m p o u n d e d q u a r t er l y . A ss u min g n o d e p os i t s or w i t h d r a w a l s a re ma d e, h o w l o n g w o u l d i t t ak e, t o t h e n e a res t ye a r, f or t h e v a l u e o f t h e a cco u n t t o re a c h 21, 090 ?

Time : 14.5

Solution steps

Translate the problem into an equation:

21090 = 8400 (1 + \frac{0.064}{4})^{4 t}

Solve for

t, 21090 = 8400 (1 + \frac{0.064}{4})^{4 t} : t = 14.5

Time : 14.5