Question

A small business repairs its store. The builders charge them $130,000 which will be paid back in monthly installments over three years at 6.80% APR. The builders will reduce this rate to 6.30% APR if they pay $2600 up front. By approximately how much will this reduce the monthly loan repayments?

Answer 1

$109.05

Step-by-step explanation:

Given :

Total Present value(PV) = $130,000

Rate(i) = 6.80% yearly = 6.80/12 = 0.566667% monthly

Number of year(n) = 3 year = 3*12 = 36 month

New rate(I) = 6.30% yearly = 6.30/12 = 0.525% monthly

New Present value(New Pv) = $130,000 - $2,600 = $ 127,400

`PV = c[(1-(1+i)^(-n))/(i) ]\\130,000 = c[(1-(1+0.0056667)^(-36))/(0.0056667) ]\\\\130,000 = c[(1-0.815931097)/(0.0056667) ]\\\\130,000 = c(0.184068903)/(0.0056667)\\ 130,000 = c(32.4825565)\\130000/32.4825565 = c\\4,002.148 = c`

`NewPV = c1[(1-(1+I)^(-n))/(I) ]\\127,400 = c1[(1-(1+0.00525)^(-36))/(0.00525) ]\\\\127,400 = c1[(1-0.828195862)/(0.00525) ]\\\\127,400 = c1(0.171804138)/(0.00525)\\ 127,400 = c1(32.7245977)\\127400/32.4825565 = c1\\3,893.09599 = c1`

difference of Payment = $4,002.148 - $3,893.09599 = $109.05