A person invests 8000 dollars in a bank. The bank pays 4.75% interest compounded daily. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 20400 dollars?

Solution

A p erso n in v es t s 8000 d o ll a rs in a bank . T h e bank p a ys 4.75% in t eres t co m p o u n d e d d ai l y . T o t h e n e a res t t e n t h o f a ye a r, h o w l o n g m u s t t h e p erso n l e a v e t h e m o n ey in t h e bank u n t i l i t re a c h es 20400 d o ll a rs ?

Time : 19.71

Solution steps

Translate the problem into an equation:

20400 = 8000 (1 + \frac{0.0475}{365})^{365 t}

Solve for

t, 20400 = 8000 (1 + \frac{0.0475}{365})^{365 t} : t = 19.71

Time : 19.71