Final answer:
To calculate the amount owed on a $5,000 loan at 4.6% annual interest rate compounded monthly after 3 years, use the compound interest formula and round to the nearest dollar, resulting in approximately $5,743.
Step-by-step explanation:
If you are planning to lend $5,000 with an annual interest rate of 4.6% compounded monthly, the amount the borrower will owe after 3 years can be calculated using the formula for compound interest: A = P(1 + r/n)nt, where:
- A is the amount that will be owed.
- P is the principal amount ($5,000 in this case).
- r is the annual interest rate (4.6% or 0.046).
- n is the number of times the interest is compounded per year (12 for monthly).
- t is the time in years (3 years).
Plugging the values into the formula, we get:
A = $5,000(1 + 0.046/12)12*3
A = $5,000(1 + 0.0038333...)36
A = $5,000 * 1.148698355...
When rounding to the nearest dollar, A is approximately $5,743.