Answer:
The amount that will be in the account three years (12 quarters) from now is $22,233.41.
Explanation:
This can be determined by considering the fact that the interest rate is compounded quarterly using the following 3 steps:
Step 1: Calculation of the amount that will be in the account one year (4 quarters) from now
This can be calculated using the following future value (FV) formula:
FV1 = PV * (1 + r)^n ........................ (1)
Where;
FV1 = Future value in one year = ?
P = Amount just deposited = $8,000
r = Quarterly interest rate = 4.0% / 4 = 0.04 / 4 = 0.01
n = number of quarters to the end of first year = 4
Substituting the values into equation (1), we have:
FV1 = $8,000 * (1 + 0.01)^4
FV1 = $8,000 * 1.04060401
FV1 = 8,324.83
Step 2: Calculation of the amount that will be in the account two years (8 quarters) from now
This can be calculated using the following future value (FV) formula:
FV2 = PV1 * (1 + r)^n ........................ (2)
Where;
FV2 = Future value in two years = ?
PV1 = Present value in one year = FV1 + Amount added after one year = 8,324.83 + $5,000 = $13,324.83
r = Quarterly interest rate = 4.0% / 4 = 0.04 / 4 = 0.01
n = number of quarters form the end of first year to the end of second year = 4
Substituting the values into equation (2), we have:
FV2 = $13,324.83 * (1 + 0.01)^4
FV2 = $13,324.83 * 1.04060401
FV2 = $13,865.87
Step 3: Calculation of the amount that will be in the account three years (12 quarters) from now
This can be calculated using the following future value (FV) formula:
FV3 = PV2 * (1 + r)^n ........................ (3)
Where;
FV3 = Future value in three years = ?
PV2 = Present value in tow years = FV2 + Amount added after two years = $13,865.87 + $7,500 = $21,365.87
r = Quarterly interest rate = 4.0% / 4 = 0.04 / 4 = 0.01
n = number of quarters form the end of second year to the end of third year = 4
Substituting the values into equation (3), we have:
FV3 = $21,365.87 * (1 + 0.01)^4
FV3 = $21,365.87 * 1.04060401
FV3 = $22,233.41
Therefore, the amount that will be in the account three years (12 quarters) from now is $22,233.41.
