# Compound Interest

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Payments of \$1,800 and \$2,400 were made on a \$10,000 variable-rate loan 18 and 30 months after the date of the loan. The interest rate was 11.5% compounded semi-annually for the first two years and 10.74% compounded monthy thereafter. What amount was owed on the loan after three years?

• Compound Interest - ,

This problem has to be solved in steps.

After 18 months (but before the first payment) the amount owed was
10,000*(1 + 0.115/2)^3 = 11,826.09
After making the first \$1800 payment, the principal owed is 10,026.09. That increases by a factor 1 + 0.115/2 at 24 months, making the principal 10,602.59.
Then the interest rate goes down. After 30 months, the amount owed is
10,602.59. x (1 + 0.1074/2)
= 11,171.95
Finally, subtract the second payment from the principal and compute the increase during the last six months of the three year period.

• Compound Interest - ,

A sum of £12,000 is invested for 5 years at an interest rate of 3.5% compounded annually. Calculate the value of the investment after 5 years.