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
periods.
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.
To determine which bank will charge the least interest, we need to calculate the effective annual interest rate (EIR) for each bank and compare them.
Let's start by calculating the EIR for Bank A with an annual interest rate of 5.7%. Since Bank A compounds annually, the effective annual interest rate is the same as the stated annual interest rate.
EIR A = 5.7%
Next, let's calculate the EIR for Bank B with a monthly compounding rate of 5.6%. We can use the formula for compound interest:
EIR B = (1 + (0.056/12))^12 - 1
Calculating this, we find:
EIR B ≈ 5.7335%
Finally, let's calculate the EIR for Bank C with a quarterly compounding rate of 5.65%. Again, we use the compound interest formula:
EIR C = (1 + (0.0565/4))^4 - 1
Calculating this, we find:
EIR C ≈ 5.7216%
Comparing the effective annual interest rates, Bank A has an EIR of 5.7%, Bank B has an EIR of 5.7335%, and Bank C has an EIR of 5.7216%.
Therefore, Bank A charges the least interest among the three options, while Bank B charges the highest interest.