Question

An interest buydown program offers to reduce interest rates by 4% from the base rate. Suppose the base rate for a loan of $8000 is 8% for 10 years. What is the monthly payment before and after the buydown? In this case, use monthly compounding, that is, the term is 120 payment periods, and the interest per month is 0.667% before and 0.333% after the buydown.

Answer 1

Answer: The monthly payment before the buydown is $71.3

The monthly payment after the buydown is $68.9

Explanation: The payment is compounding so we use compound interest;

A= P[1+(r/n)^nt]

Where;

A= Compounded amount

P = principal

r= interest rate per payment

n= number of payment per period

t= number of period.

NOTE: from our questions, the period is yearly and the payment is monthly. Therefore;

number of payment per period (n) is 12

number of payment period (t) is 10

P=$8000, r= 0.667% or 0.333%

FIND MONTHLY PAYMENT BEFORE BUYDOWN:

Step 1: find the Compounded amount to pay.

A= $8000[1+(0.00667÷12)^(12×10)]=

$8551.64 this is the total amount he has to pay for a period of 10years

Step 2: How much does he has to pay monthly for a period of 10year;

Therefore his payment will be for 120 months

$8551.64÷120= $71.3 monthly

FIND MONTHLY PAYMENT AFTER BUYDOWN:

Step 1: find the compounded amount to pay.

A= 8000[1+(0.00333÷12)^(12×10)=

$8270.85 this is the total amount he has to pay for a period of 10years

Step2: How much does he has to pay monthly for a period of 10year;

Therefore his payment will be for 120 months;

$8270.85÷120= $68.9 monthly