How much should be invested each year for 10 years to provide you with $6000 per year for the next 35 years? Assume a 5.2% interest rate. (Round your final answer to two decimal places.)


To find the amount that should be invested each year for 10 years to provide $6000 per year for the next 35 years, we will approach this problem in two parts:

1. **Calculate the present value (PV) needed at the end of 10 years** to provide an annual payout of $6000 for 35 years.
2. **Determine the annual investment amount** needed over the first 10 years to accumulate that PV amount.

### Step 1: Calculate the Present Value (PV)

To find the PV needed at the end of 10 years to provide $6000 annually for 35 years, we use the formula for the present value of an annuity:

\[
PV = P \times \frac{1 - (1 + r)^{-n}}{r}
\]

where:
- $ P = 6000 $ (annual payout)
- $ r = 0.052 $ (interest rate)
- $ n = 35 $ (number of years)

### Step 2: Calculate the Annual Investment Amount

Next, we need to find the amount to be invested annually for 10 years to reach the PV calculated in Step 1. We use the future value of an annuity formula:

\[
FV = A \times \frac{(1 + r)^n - 1}{r}
\]

where:
- $ FV = PV $ calculated in Step 1
- $ A $ is the annual investment amount
- $ r = 0.052 $ (interest rate)
- $ n = 10 $ (investment period)

Let’s calculate these values step-by-step.The present value needed at the end of 10 years to provide $6000 per year for the next 35 years is approximately \$95,814.34. 

To accumulate this amount, you need to invest approximately \$7,546.85 each year for the first 10 years.

### Follow-up Questions
1. How would the investment amount change if the interest rate was higher?
2. What if the payout period was only 25 years instead of 35 years?
3. How much would you need to invest annually if you could only invest for 5 years instead of 10?
4. What is the impact of a different interest rate during the investment period?
5. How would a lump sum investment compare to the annual investment over 10 years?

**Tip:** Understanding the relationship between the investment period, interest rate, and required payments can help in financial planning for future needs.

How much should be invested each year for 10 years to provide you with $6000 per year for the next 35 years? Assume a 5.2% interest rate. (Round your final answer to two decimal places.)

Calculate the annual investment required over 10 years to secure $6000 per year for the next 35 years with a 5.2% interest rate. This detailed guide covers the time value of money, present value, and future value of annuities, suitable for finance students and professionals.

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