You just deposited $8,000 in a bank account that pays a 4.0% interest rate, compounded quarterly. If you also add another $5,000 to the account one year (4 quarters) from now and another $7,500 to the account two years (8 quarters) from now, how much will be in the account three years (12 quarters) from now

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.

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