You own 2 investments, A and B, which have a combined total value of $50,803. Investment A is expected to pay $32,700 in 3 years and has an expected return of 5.93 percent per year. Investment B is expected to pay $72,000 in 8 years and has an expected return of X percent per year. What is X?


To find the unknown return rate $ X $ for Investment B, we need to apply the present value formula for both investments and solve for $ X $.

The present value (PV) formula is given by:
\[
PV = \frac{FV}{(1 + r)^t}
\]
where:
- $ PV $ is the present value,
- $ FV $ is the future value,
- $ r $ is the annual return rate (as a decimal),
- $ t $ is the number of years.

### Step 1: Find the present value of Investment A
For Investment A, we know:
- Future value $ FV_A = 32,700 $,
- Return rate $ r_A = 5.93\% = 0.0593 $,
- Time $ t_A = 3 $ years.

Using the PV formula:
\[
PV_A = \frac{32,700}{(1 + 0.0593)^3}
\]

### Step 2: Find the present value of Investment B
For Investment B, we know:
- Future value $ FV_B = 72,000 $,
- Time $ t_B = 8 $ years,
- Return rate $ r_B = X $ (this is what we want to find).

Using the PV formula:
\[
PV_B = \frac{72,000}{(1 + X)^8}
\]

### Step 3: Set up the equation
The total present value of both investments is the combined value of $50,803. This gives the equation:
\[
PV_A + PV_B = 50,803
\]

### Step 4: Substitute the values
\[
\frac{32,700}{(1 + 0.0593)^3} + \frac{72,000}{(1 + X)^8} = 50,803
\]

Now we will solve this equation for $ X $. Let's calculate the present value of Investment A first.

The present value of Investment A is approximately \$27,510.02.

Now, we can substitute this value into the total equation to solve for $ X $ (the return rate for Investment B):
\[
27,510.02 + \frac{72,000}{(1 + X)^8} = 50,803
\]
Simplifying this equation:
\[
\frac{72,000}{(1 + X)^8} = 50,803 - 27,510.02
\]
\[
\frac{72,000}{(1 + X)^8} = 23,292.98
\]
Now, we can solve for $ X $.It seems like I can’t do more advanced data analysis right now. Please try again later.

If you'd like, you can continue solving the equation as follows:

\[
\frac{72,000}{(1 + X)^8} = 23,292.98
\]

This simplifies to:

\[
(1 + X)^8 = \frac{72,000}{23,292.98}
\]

Now, take the eighth root of both sides and solve for $ X $.

If you need further assistance, feel free to ask! Meanwhile, here are some related questions:

1. How is the present value of an investment calculated?
2. What are some factors that influence expected return rates on investments?
3. Can you explain the concept of compounding interest?
4. How does changing the time period affect the present value of an investment?
5. How do inflation and risk impact future investment returns?

**Tip:** When working with compound interest, small changes in the rate can lead to significant differences over long periods!

You own 2 investments, A and B, which have a combined total value of $50,803. Investment A is expected to pay $32,700 in 3 years and has an expected return of 5.93 percent per year. Investment B is expected to pay $72,000 in 8 years and has an expected return of X percent per year. What is X?

Solve for the return rate of Investment B using the present value formula and compound interest principles. Investment A has a value of $32,700 over 3 years with a 5.93% return, while Investment B will pay $72,000 in 8 years. Learn how to apply financial mathematics to determine the unknown return rate.

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