Nathan invested 75,000 in an account paying an interest rate of 6.8% 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 182,800?

Solution

N a t han in v es t e d 75, 000 in an a cco u n t p a y in g an in t eres t r a t e o f 6.8% 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 182, 800 ?

Time : 13.1

Solution steps

Translate the problem into an equation:

182800 = 75000 e^{0.068 t}

Solve for

t, 182800 = 75000 e^{0.068 t} : t = 13.1

Time : 13.1