Question

A person invests 3000 dollars in a bank. The bank pays 4.25% interest compounded semi-annually. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 5600 dollars? A = P(1 + -)nt n

Answer 1

1. Define data

P = 3000 dollars

r = 4.25%

A = 5600 dollars

n = 2

2. Equation

`A=P(1+(r)/(n))^(nt)`
`5600=3000(1+0.0425/2)^(2t)`
`\begin{gathered} (5600)/(3000)=(1.02125)^(2t) \\ 1.86=(1.02125)^(2t) \end{gathered}`

Solving for t

`t=14.8\text{ years}`