Mia invested 52,000 in an account paying an interest rate of 3.1% 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 62,100?

Solution

M ia in v es t e d 52, 000 in an a cco u n t p a y in g an in t eres t r a t e o f 3.1% 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 62, 100 ?

Time : 5.73

Solution steps

Translate the problem into an equation:

62100 = 52000 e^{0.031 t}

Solve for

t, 62100 = 52000 e^{0.031 t} : t = 5.73

Time : 5.73