There Are Several Time Lags Involved When Fiscal Policy Is Applied. The First Hurdle Faced By A Government
To reach a balance of $10,600 in the account after 15 years, you would need an annual interest rate of approximately 4.05% over the last 10 years.
To determine the annual interest rate you need to earn over the last 10 years to reach a balance of $10,600 in the account, we can use the future value formula.
1. First, let’s calculate the future value of the $5,500 that you have already deposited after 5 years at an annual interest rate of 5.4 percent. We can use the formula:
Future Value = Present Value * (1 + Interest Rate)^Time
Plugging in the values:
Future Value = $5,500 * (1 + 0.054)^5
Future Value = $5,500 * 1.054^5
Future Value ≈ $6,962.14
2. Now, let’s calculate the additional amount needed to reach $10,600 in 15 years. We can subtract the future value after 5 years from the desired future value:
Additional Amount Needed = Desired Future Value – Future Value after 5 years
Additional Amount Needed = $10,600 – $6,962.14
Additional Amount Needed ≈ $3,637.86
3. Next, we can use the future value formula again to find the annual interest rate required to reach the additional amount of $3,637.86 in 10 years:
Future Value = Present Value * (1 + Interest Rate)^Time
Plugging in the values:
$3,637.86 = Present Value * (1 + Interest Rate)^10
To solve for the interest rate, we can rearrange the equation:
(1 + Interest Rate)^10 = $3,637.86 / Present Value
(1 + Interest Rate)^10 ≈ $3,637.86 / $5,500
(1 + Interest Rate)^10 ≈ 0.661343636
Taking the 10th root of both sides:
1 + Interest Rate ≈ (0.661343636)^(1/10)
Interest Rate ≈ (0.661343636)^(1/10) – 1
Calculating the interest rate:
Interest Rate ≈ 0.0405
4. Therefore, to accomplish the goal of having $10,600 in the account after 15 years, you would need to earn an annual interest rate of approximately 4.05% over the last 10 years.
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