Question

Joe negotiates an 8 year loan which requires him to pay 1200 per month for the first 4 years and 1500 per month for the remaining years. The interest rate is 13%, convertible monthly, and the first payment is due in one month. What is the amount of the loan? (round answer to nearest .01)

Answer 1

Amount of Loan = PV of Annuity

PV of Annuity:

Annuity is series of cash flows that are deposited at regular intervals for specific period of time. Here cash flows are happened at the end of the period. PV of annuity is current value of cash flows to be received at regular intervals discounted at specified int rate or discount rate to current date.

PV of annuity = Cash flow * PVAF(r%, n)

= [ $ 1200 * PVAF(1.0833%, 48) ] + [ $ 1500 * PVAF(1.0833%, 49-96 ]

= [ $ 1200 * 37.2752 ] + [ $ 1500 * 22.2229 ]

= $ 44730.23 + $ $ 33334.39

= $ 78064.62
How to calculate PVAF?

PVAF = SUm [ PVF(r%, n) ]
PVF(r%, n) = 1 / ( 1 + r)^n
r = Int rate per period
n = No. of periods

How to calculate PVAF using Excel:
=PV(Rate,NPER,-1)
Rate = Disc Rate
NPER = No.of periods

PVAF(1.0833%, 48) = 37.2752

PVAF(1.0833%, 49 - 96 ) = PVAF(1.0833%, 96 ) - PVAF(1.0833%, 48)

= 59.4981 - 37.2752

= 22.2229

Loan amount is $ 78064.62