Question

Alex Dunphy borrows $26,000 to pay for her Caltech’s tuition. The adjustable rate loan carries a 6% annual percentage rate for the first 5 years. After that the rate will be adjusted downward to 3% annually to reflect market conditions. The loan term is 20 years and payments are made monthly. What is the monthly payment after interest rate resets to 3%?

Answer 1

Initial monthly payment and balance after 5 years:

Monthly payment	=	[P × R × (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	$                                                            26,000
Rate of interest per period:
Annual rate of interest		6.000%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.06 /12 =	0.5000%
Total number of payments:
Frequency of payment	=	Once in 1 month period
Number of years of loan repayment	=	20
Total number of payments	N	20 × 12 =	240
Period payment using the formula	=	[ 26000 × 0.005 × (1+0.005)^240] / [(1+0.005 ^240 -1]
Monthly payment	=	$                                                            186.27

Loan balance	=	PV * (1+r)^n - P[(1+r)^n-1]/r
Loan amount	PV =	26,000.00
Rate of interest	r=	0.5000%
nth payment	n=	60
Payment	P=	186.27
Loan balance	=	26000*(1+0.005)^60 - 186.27*[(1+0.005)^60-1]/0.005
Loan balance	=	22,074.04

New monthly payment is:

Monthly payment	=	[P × R × (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	$                                                            22,074
Rate of interest per period:
Annual rate of interest		3.000%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.03 /12 =	0.2500%
Total number of payments:
Frequency of payment	=	Once in 1 month period
Number of years of loan repayment	=	17
Total number of payments	N	17 × 12 =	204
Period payment using the formula	=	[ 22074.04 × 0.0025 × (1+0.0025)^204] / [(1+0.0025 ^204 -1]
Monthly payment	=	$                                                            138.27

Monthly payment after five years is $138.27

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