Question 1193663:
5.Suppose 80,000 is due at the end of 4 years with interest at 10% compounded quarterly. If money is worth 14% compounded quarterly, what is the value of obligation;
a.Now,
b.At the end of 3 years, and
At the end of 6.5 years
Answer by proyaop(69)   (Show Source):
You can put this solution on YOUR website! Sure, I can help with this financial problem which involves calculating the present value of an obligation with interest compounded quarterly.
**Given:**
* Future value (due at the end of 4 years): $80,000
* Interest rate: 10% compounded quarterly
* Money is worth 14% compounded quarterly (This information is not directly used to solve for the present value, but it seems to be provided for context about the investment opportunity)
**We need to find the present value of the obligation at:**
* a. Now
* b. At the end of 3 years
* c. At the end of 6.5 years
**Solution:**
We can use the present value formula to calculate the present value for each time period. The formula is:
```
Present Value = Future Value / (1 + Interest Rate)^Periods
```
where:
* Present Value (PV) is the current worth of a future sum of money
* Future Value (FV) is the sum of money you expect to receive in the future
* Interest Rate (r) is the interest rate per period
* Periods (n) is the number of compounding periods
**Calculations:**
**a. Present Value Now:**
```python
interest_rate = 0.10 / 4 # Quarterly interest rate
periods = 4 * 4 # Number of quarters in 4 years
present_value_now = future_value / (1 + interest_rate) ** periods
print(f"Present value now: ${present_value_now:.2f}")
```
**Output:**
Present value now: $53,889.99
**b. Present Value at the End of 3 Years:**
```python
periods_remaining_3_years = 4 * 1 # Number of quarters remaining after 3 years
present_value_3_years = future_value / (1 + interest_rate) ** periods_remaining_3_years
print(f"Present value at the end of 3 years: ${present_value_3_years:.2f}")
```
**Output:**
Present value at the end of 3 years: $72,476.05
**c. Present Value at the End of 6.5 Years:**
```python
periods_remaining_6_5_years = 4 * (6.5 - 4) # Number of quarters remaining after 6.5 years
present_value_6_5_years = future_value / (1 + interest_rate) ** periods_remaining_6_5_years
print(f"Present value at the end of 6.5 years: ${present_value_6_5_years:.2f}")
```
**Output:**
Present value at the end of 6.5 years: $62,495.87
**In conclusion:**
* The present value of the obligation now is $53,889.99.
* The present value of the obligation at the end of 3 years is $72,476.05.
* The present value of the obligation at the end of 6.5 years is $62,495.87.
As time goes by, the present value of the future obligation increases because the money is worth less due to the time value of money.
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