Jim Ryan, owner of burger King restaurant assumes that his restaurant will need a new roof in 7 years. He estimates the roof will cost him $9000 at the time. What amount should Jim invest today at 6% compounded quantity to be able to pay for the roof?
To calculate the amount Jim should invest today to be able to pay for the roof in 7 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = annual interest rate (in decimal form)
n = number of times the interest is compounded per year
t = number of years
In this case, Jim needs to find the present value (P), so we can rearrange the formula as follows:
P = A / (1 + r/n)^(nt)
Given the following information:
- Future value (A) = $9000
- Annual interest rate (r) = 6% or 0.06
- Compounded once per year (n) = 1
- Time (t) = 7 years
Let's calculate the amount Jim should invest today:
P = 9000 / (1 + 0.06/1)^(1*7)
P = 9000 / (1.06)^7
P = 9000 / 1.457976
P ≈ $6176.59
Therefore, Jim should invest approximately $6176.59 today at a 6% compounded annually to be able to pay for the roof in 7 years.