The question involves computing compound interest on a $7,500 investment at a 5.8% annual rate, compounded monthly. By using the compound interest formula, the future value of the investment can be found for both 5 months and 13 years. Additionally, examples of calculating simple interest for comparison are provided.
Calculating Compound Interest
The question deals with an investment of $7,500 at a 5.8% annual interest rate, compounded monthly. Compound interest is calculated using the formula A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested or borrowed for, in years.
To find the amount after 5 months (which is roughly 0.417 years), we substitute the values into the formula and calculate the result. Similarly, the amount after 13 years can be found by using the same formula with t being 13. It is important to convert the interest rate into a decimal by dividing by 100 and to adjust the time into years when calculating compound interest.
For other examples involving simple interest: To find the total interest from a $5,000 loan at a 6% simple interest rate for three years, the total interest is calculated as Interest = Principal × rate × time, which would be $5,000 × 0.06 × 3. In another scenario, if someone receives $500 in simple interest on a $10,000 loan for five years, the interest rate is found by rearranging the simple interest formula: Interest = Principal × rate × time, which allows for solving the interest rate when the interest amount is known.