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

Answer:

$109.05

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

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

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

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