Alexandra invested 20,000 in an account paying an interest rate of 6.2% compounded annually. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach 27,200?

Solution

A l e x an d r a in v es t e d 20, 000 in an a cco u n t p a y in g an in t eres t r a t e o f 6.2% co m p o u n d e d ann u a ll 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 t e n t h o f a 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 27, 200 ?

Time : 5.11

Solution steps

Translate the problem into an equation:

27200 = 20000 (1 + \frac{0.062}{1})^{1 \cdot t}

Solve for

t, 27200 = 20000 (1 + \frac{0.062}{1})^{1 \cdot t} : t = 5.11

Time : 5.11