Alexa invested 54,000 in an account paying an interest rate of 4% 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 106,200?

Solution

A l e x a in v es t e d 54, 000 in an a cco u n t p a y in g an in t eres t r a t e o f 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 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 106, 200 ?

Time : 16.91

Solution steps

Translate the problem into an equation:

106200 = 54000 e^{0.04 t}

Solve for

t, 106200 = 54000 e^{0.04 t} : t = 16.91

Time : 16.91