Final answer:
For an investment of $20,000 for 4 years at an interest rate of 5%, the accumulated values are:
a. $22,025.00 (semiannually),
b. $22,064.90 (quarterly),
c. $22,081.77 (monthly),
d. $22,110.90 (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 (initial investment)
- r is the annual interest rate (in decimal form)
- n is the number of times the interest is compounded per year
- t is the number of years
a). Compound interest semiannually:
A = 20000(1 + 0.05/2)^(2*4)
A = $22,025.00
b). Compound interest quarterly:
A = 20000(1 + 0.05/4)^(4*4)
A = $22,064.90
c). Compound interest monthly:
A = 20000(1 + 0.05/12)^(12*4)
A = $22,081.77
d). Compound interest continuously:
A = 20000 * e^(0.05*4)
A = $22,110.90