Question 996409
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