Final answer:
To find the accumulated value of an investment, use the formula A = P(1 + r/n)^(nt), where A is the accumulated value, P is the principal amount, r is the interest rate per period, n is the number of times interest is compounded per year, and t is the number of years. For the given investment of $20,000 for 4 years at an interest rate of 4.5%, the accumulated value can be calculated for different compounding frequencies: annually, quarterly, monthly, and continuously.
Step-by-step explanation:
To find the accumulated value of an investment, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
- A is the accumulated value
- P is the principal amount (original investment)
- r is the interest rate per period
- n is the number of times that interest is compounded per year
- t is the number of years
For the given investment of $20,000 for 4 years at an interest rate of 4.5%, the accumulated value when compounded:
- Annually (n = 1): A = 20000(1 + 0.045/1)^(1 * 4)
- Quarterly (n = 4): A = 20000(1 + 0.045/4)^(4 * 4)
- Monthly (n = 12): A = 20000(1 + 0.045/12)^(12 * 4)
- Continuously (n approaches infinity): A = 20000 * e^(0.045 * 4)
Calculating these values will give you the accumulated value for each compounding frequency.