posted by Justin on .
bank a is lending money at 5.7% interest compounded annually. The rate at bank b is 5.6% compounded monthly, and the rate at bank C is 5.65% compounded quarterly. Which bank will you pay the least interest?
Bank A: Pt = Po(1+r)^n.
r = 5.7%/100% = 0.057 = APR expressed as a decimal.
n 1comp/yr * 1yr = 1 compounding period.
Pt = 1(1.057)^1 = 1.057.
Bank B: Pt = Po(1+r)^n.
r = (5.6%/12) / 100% = 0.00467 = Monthly % rate expressed as a decimal.
n = 1comp/mo * 12mo = 12 Compounding
Pt = 1(1.00467)^12 = 1.058.
Bank C: Pt = Po(1+r)^n.
r = (5.65%/4) / 100% = 0.014125 = Quarterly % rate expressed as a decimal.
n = 4comp/yr * 1yr = 4 Compounding periods.
Pt = 1(1.014125)^4 = 1.058.
The amt. charged by each bank is approximately the same.
Note: All calculations were done with the assumption that $1.00 was borrowed from each bank for a period of one year.