Question

2. A debt of $200,000 is to be amortized by making monthly payments for 20 years. If the interest rate is 4% compounded monthly, find the monthly payment.

Answer 1

Sol:

Loan present value (PV) = $200,000

Period (nper) = 20 years, Monthly = 20 x 12 = 240

Interest rate (r) = 4%, Monthly = 4%/12 = 0.3333%

To compute monthly payment:

PMT = PV/ ((1-(1/(1+r)^ⁿ))/r)

PMT = 200000 / ((1-(1/(1+0.3333%)^²⁴⁰)) / 0.3333%

PMT = 200000 / ((1-(1/(1.003333)^²⁴⁰)) / 0.003333

PMT = 200000 / 165.027598 = $1,211.96

Therefore monthly payment will be $1211.96

Alternatively to compute monthly payment we have to use PMT function in excel:

PV	-200000
nper	240
Interest rate	0.003333
PMT	$1,211.96

Working