SOLUTION: John invested $3000 that earns interest at 4% p.a. compounded monthly. Two years later, the interest rate is changed to 4.50% compounded quarterly. Determine the accumulated value

Question 1141246: John invested $3000 that earns interest at 4% p.a. compounded monthly. Two years later, the interest rate is changed to 4.50% compounded quarterly. Determine the accumulated value of the investment two years after the change.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
f = p * (1 + r) ^ n

f is the future value
p is the present value
r is the interest rate per time period
n is the number of time periods.

for the first 2 years:

p = 3000
r = 4% per year / 12 = .33333333% per month / 100 = .0033333333 per month.
n = 2 years * 12 = 24 months.

formula becomes f = 3000 * (1 + .0033333333) ^ 24 = 3249.428877.

for the second 2 years:

p = 3249.428877.
r = 4.5% / 4 = 1.125% per quarter / 100 = .01125 per quarter.
n = 2 years * 4 = 8 quarters.

formula becomes f = 3249.428877 * (1 + .01125) ^ 8 = 3553.655408.

the future value for the first 2 years becomes the present value for the second 2 years.

the time period for the first 2 years is in months.
you take the annual rate percent and divide it by 1200 to get the monthly rate.
you take the number of years and multiply them by 12 to get the number of months.

the time period for the second 2 years is in quarters.
you take the annual rate percent and divide it by 400 to get the quarterly rate.
you take the number of hyers and multiply them by 4 to get the number of quarters.

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