Question

A house is for sale for $250,000. You have a choice of two 20-year mortgage loans with monthly payments: (1) if you make a down payment of $25,000, you can obtain a loan with a 6% rate of interest or (2) if you make a down payment of $50,000, you can obtain a loan with a 5% rate of interest. What is the effective annual rate of interest on the additional $25,000 borrowed on the first loan?

Answer 1

The effective annual interest rate on the additional $25,000 borrowed on the first loan is approximately 6.1678%.

Step-by-step explanation:

To calculate the effective annual rate of interest on the additional $25,000 borrowed on the first loan, we can use the formula for calculating the effective annual interest rate:

Effective Annual Interest Rate = (1 + (Annual Interest Rate / Number of Compounding Periods))^Number of Compounding Periods - 1

For the first loan, the annual interest rate is 6% and the number of compounding periods is 12 (since it is a monthly payment). Plugging the values into the formula, we get:

Effective Annual Interest Rate on first loan =
`(1 + (0.06 / 12))^(12)` - 1 = 0.061678

The effective annual interest rate on the additional $25,000 borrowed on the first loan is approximately 6.1678%.

Answer 2

The effective annual rate of interest on the additional $25,000 borrowed on the first loan is 12.95%

Step-by-step explanation:

the loan amount is $250,000 and the period is 20 years.

1.

down payment of $50,000 and the interest rate is 6% per annum

the loan amount = $250,000 - $50,000

= $200,000

period = 20*12

= 240 months

rate = 5%/12

= 0.4167% per month

monthly payment = $1,319.91

difference between the payments in 1 and in 2 = 1611.97 - 1319.91

= $292.06

additional down payment is $25,000

2.

down payment of $25,000 and the interest rate is 6% per annum

the loan amount = $250,000 - $25,000

= $225,000

period = 20*12

= 240 months

rate = 6%/12

= 0.5% per month

monthly payment = $1,611.97

difference between the payments in 1 and in 2 = 1611.97 - 1319.91

= $292.06

additional down payment is $25,000

the effective annual rate = [(292.06/25000)*12]*100

= 12.95%

Therefore, The effective annual rate of interest on the additional $25,000 borrowed on the first loan is 12.95%