Question

Determine the payment to amortize the debt. (round your answer to the nearest cent.)

Quartey payments on $15,500 at 3.5% for 6 years.

Find the unpaid balance on the debt. (Round your answer to the nearest cent)

After 7 years of monthly payments on $180,000 at 3% for 25 years.

Answer 1

Amortized amount P = $15500

rate r = 3.5% = 3.5/100 = 0.035

and compounded quarterly so r = 0.035/4 = 0.00875

And number of payments = 6 x 4 = 24

PMT = [ p x r x (1+r)^t ] / [(1+r)^t-1]

PMT = [15500 x 0.00875 x (1+0.00875)²⁴ ] / [(1+0.00875)²⁴-1]

PMT = [135.625 x 1.23255] / [1.23255 - 1]

PMT = [167.1645] / [0.23255]

PMT = 718.8329 ~ 719

So quarterly payment amount is $719

First we need to find the monthly payment

Amortized amount P = $180000

rate r = 3% = 3/100 = 0.03

and compounded monthly so r = 0.03/12 = 0.0025

And number of payments = 25 x 12 = 300

PMT = [ p x r x (1+r)^t ] / [(1+r)^t-1]

PMT = [180000 x 0.0025 x (1+0.0025)³⁰⁰ ] / [(1+0.0025)³⁰⁰-1]

PMT = [450 x 2.11501] / [2.11501 - 1]

PMT = [951.7545] / [1.11501]

PMT = 853.5838 ~ 853.6

So quarterly payment amount is $853.6

So we have to calculate the outstanding loan balance after 7 years which is 84 payments by calculating the present value of the remaining installments, using the present value of an annuity formula

Pmt = Periodic payment = $853.6

i = interest rate per period = 0.0025

n = Number of remaining payments = 300 – 84 = 216

we can use below formula

PV = Pmt x [(1 - 1 / (1 + i)ⁿ)] / i

PV = 853.6 x [(1 - 1 / (1 + 0.0025)²¹⁶)] / (0.0025)

PV = 853.6 X [(1-1/(1.0025)²¹⁶)]/( 0.0025)

PV = 853.6 X [1-1/(1.71485)]/( 0.0025)

PV = 853.6 X [1-0.58314]/( 0.0025)

PV = 853.6 X [0.41686]/( 0.0025)

PV = 853.6 X 166.744

PV = 142332.6784 ~ 142332.7

So the present value of annuity is $142332.7

The balance unpaid after 7 years of payments made is = $142332.7