Olivia invested 500 in an account paying an interest rate of 2.4% compounded continuously. 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 650?

Solution

Ol i v ia in v es t e d 500 in an a cco u n t p a y in g an in t eres t r a t e o f 2.4% co m p o u n d e d co n t in u o u s 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 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 650 ?

Time : 10.93

Solution steps

Translate the problem into an equation:

650 = 500 e^{0.024 t}

Solve for

t, 650 = 500 e^{0.024 t} : t = 10.93

Time : 10.93