Question

Calculate the present value of the annuity. (round your answer to the nearest cent.)

$1800 monthly at 6.1% for 30 years.

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

Monthly payments on $170,000 at 3% for 25 years.

Answer 1

Pmt = Periodic payment = $1800

i = interest rate per period = 6.1% = 6.1/100 = 0.061

and compounded monthly so I = 0.061/2 = 0.0050833

n = Number of payments = 30 years = 30 x12 = 360

we can use below formula

PV = Pmt x [(1 - 1 / (1 + i)ⁿ)] / i

PV = 1800 x [(1 - 1 / (1 + 0.0050833)³⁶⁰)] / (0.0050833)

PV = 1800 X [(1-1/(1.0050833)³⁶⁰)]/( 0.0050833)

PV = 1800 X [1-1/(6.20498)]/( 0.0050833)

PV = 1800 X [1-0.16116]/( 0.0050833)

PV = 1800 X [0.83884]/( 0.0050833)

PV = 1800 X 165.018787

PV = 297033.816 ~ 297034

So the present value of annuity is $297034

Amortized amount P = $170000

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 = [170000 x 0.0025x (1+0.0025)³⁰⁰ ] / [(1+0.0025)³⁰⁰-1]

PMT = [425 x 2.11501] / [2.11501 - 1]

PMT = [898.879] / [1.11501]

PMT = 806.1625 ~ 806

So MONTHLY PAYMENT amount is $806