Final answer:
a. The after-tax interest for the first year of Hassnein's investment is $599.40. b. The after-tax interest for the second year, when Hassnein withdraws cash to pay the tax on the interest, is $1,202.71. c. After 4 years, Hassnein will have $34,157.86 in the account. d. After 7 years, Hassnein will have $36,890.37 in the account.
Step-by-step explanation:
a. To calculate the after-tax interest for the first year of Hassnein's investment, we need to multiply the interest rate by 1 minus the marginal tax rate. The after-tax interest for the first year is calculated as follows: $31,250 * (0.024 * (1 - 0.22)) = $599.40.
b. For the second year, Hassnein will withdraw enough cash to pay the tax on the interest. So the after-tax interest for the second year is calculated as follows: ($31,250 + $599.40) * (0.024 * (1 - 0.22)) = $1,202.71.
c. To calculate the amount in the account after 4 years, we need to calculate the compound interest. The formula to calculate compound interest is: A = P(1+r/n)^(nt), where A is the amount, P is the principal (initial amount), r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. So the amount in the account after 4 years is given by: $31,250 * (1 + 0.024/1)^(1*4) = $34,157.86.
d. Similarly, to calculate the amount in the account after 7 years, we use the same formula: $31,250 * (1 + 0.024/1)^(1*7) = $36,890.37.