Question

Suppose that you have just borrowed $195,000 in the form of a 10 year mortgage. The loan has an annual interest rate of 5.375% with monthly payments and monthly compounding.

*** I NEED TO KNOW HOW TO SOLVE THIS ON A CALCULATOR. I AM USING A HP-10B2+

a. What will your monthly payment be for this loan?

b. What will the balance on this loan be at the end of the 5th year?

c. How much interest will you pay in the 7th year of this loan?

d. How much of the 77th payment will consist of principal?

Answer 1

a. What will your monthly payment be for this loan?

Monthly payment (PMT) on loan can be calculated with the help of PV of an Annuity formula

PV = PMT * [1-(1+i) ^-n)]/i

Where,

Present value (PV) = $195,000

PMT = Monthly payment =?

n = N = number of payments = 12 *10 years = 120 payments

i = annual interest rate = 5.375%; therefore monthly interest rate = 5.375%/12 = 0.448% per month

Therefore,

$195,000 = PMT* [1- (1+0.448%) ^-120]/0.448%

= $2,104.20

b. What will the balance on this loan be at the end of the 5th year?

PV = PMT * [1-(1+i) ^-n)]/i

Where,

The balance on this loan at the end of the 5th year or Present value (PV) =?

PMT = Monthly payment =$2,104.20

n = N = number of remaining payments = 12 *5 years = 60 payments

i = annual interest rate = 5.375%; therefore monthly interest rate = 5.375%/12 = 0.448% per month

Therefore,

The balance on this loan at the end of the 5th year =$2,104.20* [1- (1+0.448%) ^-60]/0.448%

= $110,494.54

c. How much interest will you pay in the 7th year of this loan?

The interest you will pay in the 7th year of this loan = total payment in 7^th year – principal payment in 7^th year

= 12 * Monthly payment – (the balance on this loan be at the end of the 6th year - the balance on this loan be at the end of the 7th year)

= 12 *$2,104.20 – ({$2,104.20* [1- (1+0.448%) ^-48]/0.448%} - {$2,104.20* [1- (1+0.448%) ^-36]/0.448%})

= $25,250.46 - {$90,700.24 -$69,815.40}

= $25,250.46 - $20,884.85

= $4,365.61

d. How much of the 77th payment will consist of principal?

We have following formula to calculate nth principal payment

Principal paid (nth payment) = Total monthly Payment / [1+R) ^ (N-n+1)]

Where,

Principal paid (77th payment) =?

Total monthly Payment =$2,104.20

Monthly interest rate (R) = 0.448%

Total number of payments (N) = 120

Payment for with principal amount (n) = 77

Therefore,

Principal paid (77th payment) = =$2,104.20/ [1+0.448%) ^ (120-77+1)]

=$1,728.57