Question

The price of a small cabin is ​$65 comma 000. The bank requires a​ 5% down payment. The buyer is offered two mortgage​ options: 20-year fixed at 7.5​% or​ 30-year fixed at 7.5​%. Calculate the amount of interest paid for each option. How much does the buyer save in interest with the​ 20-year option?

Answer 1

Price =65000
PV of loan =Price*(1-5%) =65000*(1-5%) =61750

Number of years =20
Rate =7.5%
Periodic Payment =PV/((1-(1+r)^-n)/r =61750/((1-(1+7.5%)^-20)/7.5%)=6057.192833
Interest paid =Periodic Payments *Number of Period -PV =6057.192833*20-61750 =59393.8567

Number of years =30
Rate =7.5%
Periodic Payment =PV/((1-(1+r)^-n)/r =61750/((1-(1+7.5%)^-30)/7.5%)=5228.4488
Interest paid =Periodic Payments *Number of Period -PV =5228.4488*30-61750 =95103.4640

Interest saved in interest with 20 year option =95103.4640-59393.8567=35709.61