Question

What is the monthly payment on a 15 year, $350,000 mortgage loan, where interest rate is 3% per year,

1. Compounded annually
2. Compounded monthly
3. Compounded daily
4. What are effective annual rates for 1,2, and 3 above?

Answer 1

1. Rate = 3%
PV = 350,000
Number of periods = 15
Yearly Payments = 350,000/((1-(1+3%)^-15 /3% = 29,318.30
Monthly Payment = 29,318.30/12 = 2443,19

EAR at annual compounding = 3%

2. Monthly compounding
Rate = 3%/12 =0.25%
PV = 350,000
Number of periods = 15*12 = 180
Monthly Payments = 350,000/((1-(1+0.25%)^-180/0.25% = 2,417.40

EAR at annual compounding = (1+0.25%)¹²-1 = 3.04%

3. Compounded Daily
Rate = 3%/365
PV = 350,000
Number of periods = 15*365
Payments = 30* 350,000/((1-(1+3%/365)^-365*15/(3%/365) = 2381.65

EAR at annual compounding = (1+3%/365⁾³⁶⁵-1 = 3.05%

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