Brody invested 2,800 in an account paying an interest rate of 2.7% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach 3,560?

Solution

B ro d y in v es t e d 2, 800 in an a cco u n t p a y in g an in t eres t r a t e o f 2.7% 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 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 3, 560 ?

Time : 8.89

Solution steps

Translate the problem into an equation:

3560 = 2800 e^{0.027 t}

Solve for

t, 3560 = 2800 e^{0.027 t} : t = 8.89

Time : 8.89