SOLUTION: Jerod hopes to earn $800 in interest in 2 years time from $40,000 that he has available to invest. To decide if it's feasible to do this by investing in an account that compounds

Question 1170313: Jerod hopes to earn $800 in interest in 2 years time from $40,000 that he has available to invest. To decide if it's feasible to do this by investing in an account that compounds quarterly, he needs to determine the annual interest rate such an account would have to offer for him to meet his goal. What would the annual rate of interest have to be? Round to two decimal places.

Found 2 solutions by josgarithmetic, Theo:
Answer by josgarithmetic(39630) (Show Source): You can put this solution on YOUR website!
If r is for the QUARTERLY compounding period rate and for 8 periods (for the two years), then .

For YEARLY rate, 0.99%
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
formula to use is f = p * (1 + r) ^ n
f is the future value
p is the present value
n is the number of time periods
r is the interest rate per time periods.

your inputs are:
f = 40,800 (= 40,000 + 800 interest)
p = 40,000
n = 2 year * 4 quarters per year = 8
r = what you want to find

formula becomes 40,800 = 40,000 * (1 + r) ^ 8
divide both sides of the equation by 40,000 to get:
40,800/40,000 = (1+r)^8
take the 8th root of both sides of the equation to get:
(40,800/40,000)^(1/8) = 1+r.
subtract 1 from both sides of the equation and solve for r to get:
r = (40,800)/40,00)^(1/8)-1 = .0024783946 per quarter.
multiply this by 4 to get:
r = .00991357826 per year.
round this to 2 decimal places to get:
r = .01 per year.

if you show it as a percent first and then round to 2 decimal places, you will get:
r = .00991357826 per year * 100 = .991357826% per year.
round to 2 decimal places to get:
r = .99% per year.

the answer depends on whether you have to show it as a rate or as a percent before you round it.

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