Question

Assume that your aunt sold her house on December 31, and to help close the sale she took a second mortgage in the amount of $10,000 as part of the payment. The mortgage has a quoted (or nominal) interest rate of 12%; it calls for payments every 6 months, beginning on June 30, and is to be amortized over 10 years. Now, 1 year later, your aunt must inform the IRS and the person who bought the house about the interest that was included in the two payments made during the year. (This interest will be income to your aunt and a deduction to the buyer of the house.) To the closest cent, what is the total amount of interest that was paid during the first year

Answer 1

Total interest paid during the first year: $1,183.69

Step-by-step explanation:

First, we need to know the installment amount:

`PV / (1-(1+r)^(-time) )/(rate) = C\\`

PV 10,000.00

time 20

rate 0.06

`10000 / (1-(1+0.06)^(-20) )/(0.06) = C\\`

C $ 871.85

now we calcualte the interest and amortization made in the first payment:

interest: 10,000 x 6% = 600

Amortization 871,85 - 600 = 271,85

Principal at second installment:

10,000 - 271.85 = 9,728.15

Interest 9,728.15 x 0.06 = 583,69

Total interest: 583,69 + 600 = 1.183,69