Annabelle invested 5,900 in an account paying an interest rate of 2% 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 7,440?

Solution

A nnab e ll e in v es t e d 5, 900 in an a cco u n t p a y in g an in t eres t r a t e o f 2% 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 7, 440 ?

Time : 11.6

Solution steps

Translate the problem into an equation:

7440 = 5900 e^{0.02 t}

Solve for

t, 7440 = 5900 e^{0.02 t} : t = 11.6

Time : 11.6