Jayden invested 22,000 in an account paying an interest rate of 2.5% 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 30,400?

Solution

J a y d e n in v es t e d 22, 000 in an a cco u n t p a y in g an in t eres t r a t e o f 2.5% 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 30, 400 ?

Time : 12.94

Solution steps

Translate the problem into an equation:

30400 = 22000 e^{0.025 t}

Solve for

t, 30400 = 22000 e^{0.025 t} : t = 12.94

Time : 12.94