3. Carolina is considering a purchase of a new warehouse for its expanding parts

Question

3. Carolina is considering a purchase of a new warehouse for its expanding parts division. Purchase will be financed with a $4,000,000 loan. The term of the loan: 15 years, amortizing (monthly payments), APR of 4.80%. The first payment is due one month from the day loan is taken. a) What will be the amount of each monthly payment? b) Alternatively, Carolina can use 20-year, monthly amortizing loan with 5.40% APR. How much more in total interest Carolina will pay if it goes with 20-year rather than 15-year loan? (Assume no pre-payments, refinancing, late payments etc.)

Explanation / Answer

Step-1;Calculation of Interest payments over 15 Years term a. Monthly Payment = Loan amount / Present Value of annuity of 1 = $          40,00,000.00 /        128.137046 = $                31,216.58 Working: Present Value of annuity of 1 = (1-(1+i)^-n)/i Where, = (1-(1+0.004)^-180)/0.004 i 4.80%/12 = 0.004 =                 128.137046 n 15*12 = 180 b. Total Payments over 15 years = Monthly Payments x Months in 15 years = $                31,216.58 x 180 = $          56,18,983.93 c. Total Interest Payment = Total Payment over 15 years - Loan Amount = $          56,18,983.93 - $ 40,00,000.00 = $          16,18,983.93 Step-2:Calculation of Interest payments over 20 Years a. Monthly Payment = Loan amount / Present Value of annuity of 1 = $          40,00,000.00 /        146.573495 = $                27,290.06 Working: Present Value of annuity of 1 = (1-(1+i)^-n)/i Where, = (1-(1+0.0045)^-240)/0.0045 i 5.40%/12 = 0.0045 =                 146.573495 n 20*12 = 240 b. Total Payments over 15 years = Monthly Payments x Months in 15 years = $                27,290.06 x 240 = $          65,49,615.27 c. Total Interest Payment = Total Payment over 15 years - Loan Amount = $          65,49,615.27 - $ 40,00,000.00 = $          25,49,615.27 Step-3:Calculation of excess Interest payment over 20 years term Interest Paid over 20 years $          25,49,615.27 Less:Interest Paymet over 15 years $          16,18,983.93 Excess Interest Payment made $             9,30,631.33

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