Use the formula for present value of money to calculate the amount you need to invest now in one lump sum in order to have after 10 years with an APR of
compounded quarterly. Round your answer to the nearest cent, if necessary.
Formulas

Question

Use the formula for present value of money to calculate the amount you need to invest now in one lump sum in order to have

after 10 years with an APR of

compounded quarterly. Round your answer to the nearest cent, if necessary.
Formulas

UpStudy AI · Accepted Answer

To determine the amount you need to invest today (Present Value, **PV**) to have \$25,000 in 10 years (**Future Value, FV**) with an Annual Percentage Rate (APR) of 6% compounded quarterly, we can use the **Present Value formula**:

$$
PV = \frac{FV}{\left(1 + \frac{r}{n}\right)^{n \cdot t}}
$$

### **Where:**
- **FV** = \$25,000 (Future Value)
- **r** = 6% or 0.06 (Annual Interest Rate)
- **n** = 4 (Number of compounding periods per year, since it's quarterly)
- **t** = 10 years (Time)

### **Step-by-Step Calculation:**

1. **Identify the Variables:**
   $$
   FV = 25,000 \
   r = 0.06 \
   n = 4 \
   t = 10
   $$

2. **Plug the Values into the Formula:**
   $$
   PV = \frac{25,000}{\left(1 + \frac{0.06}{4}\right)^{4 \times 10}}
   $$

3. **Simplify Inside the Parentheses:**
   $$
   1 + \frac{0.06}{4} = 1 + 0.015 = 1.015
   $$

4. **Calculate the Exponent:**
   $$
   4 \times 10 = 40
   $$
   $$
   1.015^{40} \approx 1.8140
   $$

5. **Divide the Future Value by the Compounded Factor:**
   $$
   PV = \frac{25,000}{1.8140} \approx 13,763.91
   $$

### **Final Answer:**
You need to invest **\$13,763.91** today to have \$25,000 in 10 years with a 6% APR compounded quarterly.
You need to invest \$13,763.91 today to have \$25,000 in 10 years with a 6% APR compounded quarterly.

Use the formula for present value of money to calculate the amount you need to invest now in one lump sum in order to have after 10 years with an APR of
compounded quarterly. Round your answer to the nearest cent, if necessary.
Formulas

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Use the formula for present value of money to calculate the amount you need to invest now in one lump sum in order to have after 10 years with an APR of compounded quarterly. Round your answer to the nearest cent, if necessary. Formulas

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Use the formula for present value of money to calculate the amount you need to invest now in one lump sum in order to have after 10 years with an APR of
compounded quarterly. Round your answer to the nearest cent, if necessary.
Formulas