Question

Mobile Health needs to replace its mobile medical unit to continue providing diagnostic services and preventative medicine to city residents. The van costs $120,000, and a bank is willing to lend the nonprofit the money at a 6% interest rate for 5 years. Payments are due at the end of each month, and interest is compounded monthly. How much should you budget for the monthly payment?

Note: Need to solve without using PMI

Answer 1

Loan Amount P = $120000

Interest Rate = 6% or 0.06/12 monthly

Number of payment periods = n = 5*12 = 60 months

Let monthly payments made be X

Hence, the sum of present value of monthly payments must be equal to the value of the loan amount

=> X/(1+r) + X/(1+r)² +....+ X/(1+r)^N = P

=> X[1- (1+r)^-N]/r = P

=> X = rP(1+r)^N/[(1+r)^N-1]

=> Monthly Payments =  rP(1+r)^N/[(1+r)^N-1]

= 120000*( 0.06/12)*(1+ 0.06/12)⁶⁰/((1+ 0.06/12)⁶⁰-1) = $2319.94

Hence, you should budget $2319.94 for monthly payments