Question

28. calculate  the present value of the annuity. (Round your answer to the nearest cent.)

$1300 monthly at 6.3% for 30 years.

29. determine the payment to amortize the debt. (Round your answer to the nearest cent.)

Monthly payments on $130,000 at 4% for 25 years.

Answer 1

Pmt = Periodic monthly payment = $1300

i = Mortgage interest rate per period = 6.3% = 6.3/100 = 0.063

and compounded monthly so I = 0.063/12  = 0.00525

n = Number of payments = 30 x 12 = 360

we can use below formula

PV = Pmt x [(1 - 1 / (1 + i)ⁿ)] / i

PV = 1300 x [(1 - 1 / (1 + 0.00525)³⁶⁰)] / (0.00525)

PV = 1300 X [(1-1/(1.00525)³⁶⁰)]/( 0.00525)

PV = 1300 X [1-1/(6.5867)]/( 0.00525)

PV = 1300 X [1-0.1518]/( 0.00525)

PV = 1300 X [0.8482]/( 0.00525)

PV = 1300 X 161.5619

PV = 210030.47

So the present value of annuity is $210030.47

Amortized amount P = $130000

rate r = 4/100 = 0.04

and compounded monthly so r = 0.04/12 = 0.003333

And number of payments = 25 x 12 = 300

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

PMT  = [130000 x 0.003333x (1+0.003333)³⁰⁰ ] / [(1+0.003333)³⁰⁰-1]

PMT = [433.29 x 2.71349] / [2.71349 - 1]

PMT = [1175.728] / [1.71349]

PMT = 686.1598 ~ 686.16

So MONTHLY PAYMENT  amount is $686.16