You are able to obtain a $750,000 loan. Interest rate is 20% per year compounded

Question

You are able to obtain a $750,000 loan. Interest rate is 20% per year compounded monthly. You don't have to start paying until the end of the first month of the third year, with equal monthly payments thereafter for four complete years or forty-eight monthly payments.

a. Compute the monthly payments of the loan.

b. Compute the total amount of interest paid to the lender.

c. You decide to pay off the debt immediately after making the thirty-sixth payment in month 48, how much must you pay to the lender?

Explanation / Answer

Answer:

(a) Value of loan at the end to Year 2(or say beginning of year 3) :

Using formula :

Future value = Present value ( 1+ r)^n

Here Present value = $750000

r = 20% Per year = 20%/12 =1.66% per month = 0.0166

n = 2 years = 2*12 = 24months

Hence FV = 750000 *(1+0.0166)^24 = $1113432.24

Now the installment shall be paid from the end of first month of year 3 and shall be paid for next 48 months

Now calculation of installment using present value of annuity formula:

P = r (PV) / {1-(1+r)^-n}

Here P = Installment

PV = Present value = $1113432.24

r= rate of interest = 0.0166

n = period = 48 months

Hence,

P = [0.01668*(1113432.24)] / [1-{(1+0.0166)^(-48)}]

P = $33997.77

(b) Total amount of installments paid = $33997.77 * 48 = $1631892.96

Less: loan amount = $750000

Total interest paid =$1631892.96 - $750000 = $881892.96

(c) IF we decide to pay off the debt immediately after making the thirty-sixth payment in month 48, it means there are 12 more installments remaining so we need to pay the present value of those remaining installments.

Using formula :

Present value = P [{1-(1+r)^-n} / {r}]

Here P = Installment =$33997.77

r= rate of interest = 0.0166

n = period = 12 months

hence

Present value = 33997.77 [{1-(1+0.0166)^-12} / {0.0166}]

Hence we must pay to the lender = $367162

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