Question

Tom hopes to earn $700 in interest in 4.1 years time from $35,000 that he has available to invest. To decide if it's feasible to do this by investing in an account that compounds annually, he needs to determine the annual interest rate such an account would have to offer fo him to meet his goal. What would the annual rate of interest have to be

Answer 1

0.48%

Explanation:

Since you're dealing with an account that compounds annually, use the formula
`A=P(1+r)^t`.
A = the final Amount in the account
P = the Principal (amount invested)
r = the annual interest Rate, as a decimal
t = Time in years

1. Set up:

`35700=35000(1+r)^(4.1)`

2. Use Inverse Operations to isolate r:

`(35700)/(35000)=(1+r)^(4.1)`

`1.02=(1+r)^(4.1)`

`\sqrt[4.1]{1.02}=1+r`

`\sqrt[4.1]{1.02}-1=r`
r ≈ 0.0048

3. Change the decimal to a percent (multiply by 100).