SOLUTION: Bank 'A' provides loan at 5% per annum at simple interest and bank 'B' provides loan at the same rate for the same period compounded annually. Then, which bank is preferable for a

Question 996409: Bank 'A' provides loan at 5% per annum at simple interest and bank 'B' provides loan at the same rate for the same period compounded annually. Then, which bank is preferable for a person to take a loan?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the bank that compounds annually is the better choice because you are earning interest on interest.

formula for future value of a present amount for n years assuming simple interest is:

f = p * (1 + x*n)

formula for future value of a present amount for n year at x interest rate assuming annual compounding is:

f = p * (1+x)^n

for example:

assume 1000 investment at 5% per year.

simple interest gets you:

f = 1000 * (1+.05*5) = 1250

compound interest gets you:

f = 1000 * (1+.05)^5 = 1276.28

with simple interest, the interest each year is calculated off the original investment * the interest rate.

you get 1000 + 1000*.05 + 1000*.05 + 1000*.05 + 1000*.05 + 1000*.05

total interest = 50 + 50 + 50 + 50 + 50 = 250

with compound interest. the interest rate each year is calculated off the original investment plus the total interest earned the previous year.

you get 1000 + 1000*.05 + 1050*.05 + 1102.5*.05 + 1157.625*.05 + 1215.50625*.05

total interest = 50 + 52.5 + 55.125 + 57.88125 + 60.7753125 = 276.2815625

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