Lydia invested 8,300 in an account paying an interest rate of 2.2% compounded daily. 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 12,690?

Solution

L y d ia in v es t e d 8, 300 in an a cco u n t p a y in g an in t eres t r a t e o f 2.2% co m p o u n d e d d ai 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 12, 690 ?

Time : 19.3

Solution steps

Translate the problem into an equation:

12690 = 8300 (1 + \frac{0.022}{365})^{365 t}

Solve for

t, 12690 = 8300 (1 + \frac{0.022}{365})^{365 t} : t = 19.3

Time : 19.3