Compound Interest
posted by Sat .
Payments of $1,800 and $2,400 were made on a $10,000 variablerate loan 18 and 30 months after the date of the loan. The interest rate was 11.5% compounded semiannually for the first two years and 10.74% compounded monthy thereafter. What amount was owed on the loan after three years?

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. 
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.