Question

You borrowed $150,000 to purchase a house. You fixed the loan's interest rate for 12 months at a time. Your loan had an initial term of 23 years with monthly payments. You repaid your loan early, at the end of 4 years. The fixed interest rates were as follows: Year 1: 5.75\%; Year 2: 4.75\%; Year 3: 5.49\%; Year 4: 3.29\%. Calculate the effective interest rate (borrowing cost) on this loan. Enter your answer without the percentage [\%] sign, rounded to 4 decimal places (e.g. 10.4567).

Answer 1

The effective interest rate on the loan is calculated as a simple average of the annual fixed interest rates over the 4-year term, resulting in an interest rate of 4.8200.

Step-by-step explanation:

To calculate the effective interest rate (borrowing cost) on the loan, one would typically use the formula for the annual percentage rate (APR), which considers the compounding interest across different periods. However, since this question provides fixed interest rates for each year and specifies the loan was repaid in full at the end of 4 years, we can simplify the calculation by taking a weighted average of the fixed interest rates for the years the loan was held. This simpler method does not account for the effects of compounding but gives a straightforward average cost of borrowing.

The fixed interest rates were as follows:

• Year 1: 5.75%
• Year 2: 4.75%
• Year 3: 5.49%
• Year 4: 3.29%

This gives us an average interest rate (simple calculation without compounding):

Effective Interest Rate = (5.75% + 4.75% + 5.49% + 3.29%) / 4

= (19.28%) / 4

= 4.82%

Thus, the effective interest rate, rounded to four decimal places, is 4.8200.