I find it easiest to use the Excel PMT or Payment function for these type problems.
PMT Function in Excel: =PMT(rate,nper,pv)
For this problem, a 30% down payment would be equal to $127,500 which would bring the total principal financed to $297,500.
Where our interest rate is 4.94% annually, our number of payments is monthly for 30 years, so 30 x 12 = 360 total, and our present value or financed value is $297,500.
Applied PMT Function in Excel: =PMT(0.0494/12, 360, 297,500)
This formula gives us the total monthly payment. Total cost is calculated by simply multiplying monthly payment by the number of payments. Total interest paid is calculated by simply subtracting the loan amount from the total cost that we just calculated.
Monthly Payment: $1,586.15
Total Cost: $1,586.15 x 360 = $571,015.08
Total Interest Paid: $571,015.08 – $297,500.00 = $273,515.08
To determine the money saved if the loan duration were to be reduced to 15 years, simply change that in the PMT function. Meaning, instead of 360 payment periods, there are now 180 (15 years x 12 months per year = 180 total).
By doing so, it can be seen that the monthly payment increases to $2,343.32. The Total cost decreases to $421,798.16. Finally, the total interest paid decreases to $124,298.16.
Hope this helps!