Sophie invested 420 in an account paying an interest rate of 1.6% compounded monthly. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach 570?

Solution

S o p hi e in v es t e d 420 in an a cco u n t p a y in g an in t eres t r a t e o f 1.6% co m p o u n d e d m o n t h 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 570 ?

Time : 19.1

Solution steps

Translate the problem into an equation:

570 = 420 (1 + \frac{0.016}{12})^{12 t}

Solve for

t, 570 = 420 (1 + \frac{0.016}{12})^{12 t} : t = 19.1

Time : 19.1