SOLUTION: A corporation issues a RM2, 500, 000 piece of commercial paper that comes due in 2 years. If it sets up a sinking fund with an institution that pays 8%, what will its quarterly pay

Question 1162507: A corporation issues a RM2, 500, 000 piece of commercial paper that comes due in 2 years. If it sets up a sinking fund with an institution that pays 8%, what will its quarterly payment be? Set up a schedule showing the accumulation of the assets in this sinking fund.
Answer by CPhill(2264) (Show Source): You can put this solution on YOUR website!
```python?code_reference&code_event_index=2
import pandas as pd
# Given values
fv = 2500000
annual_rate = 0.08
compounding_frequency = 4
years = 2
n = years * compounding_frequency
i = annual_rate / compounding_frequency
# Calculate Payment (PMT)
# FV = PMT * ((1 + i)**n - 1) / i
pmt = (fv * i) / ((1 + i)**n - 1)
# Sinking Fund Schedule
schedule = []
balance = 0
for period in range(1, n + 1):
interest = balance * i
increase = pmt + interest
balance += increase
schedule.append({
"Quarter": period,
"Payment": pmt,
"Interest Earned": interest,
"Increase in Fund": increase,
"Fund Balance": balance
})
df_schedule = pd.DataFrame(schedule)
# Format for output
print(f"Quarterly Payment: {pmt}")
print(df_schedule)
# Write to CSV
df_schedule.to_csv("sinking_fund_schedule.csv", index=False)

```
```text?code_stdout&code_event_index=2
Quarterly Payment: 291274.49783440644
Quarter Payment Interest Earned Increase in Fund Fund Balance
0 1 291274.497834 0.000000 291274.497834 2.912745e+05
1 2 291274.497834 5825.489957 297099.987791 5.883745e+05
2 3 291274.497834 11767.489713 303041.987547 8.914165e+05
3 4 291274.497834 17828.329463 309102.827298 1.200519e+06
4 5 291274.497834 24010.386009 315284.883844 1.515804e+06
5 6 291274.497834 30316.083686 321590.581521 1.837395e+06
6 7 291274.497834 36747.895317 328022.393151 2.165417e+06
7 8 291274.497834 43308.343180 334582.841014 2.500000e+06
```
[file-tag: code-generated-file-0-1776522428876279223]
To calculate the quarterly payment for the sinking fund, we use the formula for the future value of an ordinary annuity:
$$FV = PMT \times \frac{(1 + i)^n - 1}{i}$$
Where:
* $FV = \text{RM } 2,500,000$ (The future amount needed)
* $r = 0.08$ (Annual interest rate)
* $m = 4$ (Quarterly compounding)
* $i = \frac{r}{m} = \frac{0.08}{4} = 0.02$ (Quarterly interest rate)
* $t = 2 \text{ years}$
* $n = t \times m = 2 \times 4 = 8$ (Total number of quarterly payments)
### 1. Quarterly Payment Calculation
Rearranging the formula to solve for $PMT$:
$$PMT = \frac{FV \times i}{(1 + i)^n - 1}$$
$$PMT = \frac{2,500,000 \times 0.02}{(1 + 0.02)^8 - 1}$$
$$PMT = \frac{50,000}{(1.02)^8 - 1}$$
$$PMT \approx \text{RM } 291,274.50$$
The quarterly payment required is **RM 291,274.50**.
### 2. Sinking Fund Schedule
The following schedule shows the accumulation of assets in the sinking fund over the 2-year period.
| Quarter | Payment (RM) | Interest Earned (RM) | Increase in Fund (RM) | Fund Balance (RM) |
| :--- | :--- | :--- | :--- | :--- |
| 1 | 291,274.50 | 0.00 | 291,274.50 | 291,274.50 |
| 2 | 291,274.50 | 5,825.49 | 297,099.99 | 588,374.49 |
| 3 | 291,274.50 | 11,767.49 | 303,041.99 | 891,416.48 |
| 4 | 291,274.50 | 17,828.33 | 309,102.83 | 1,200,519.31 |
| 5 | 291,274.50 | 24,010.39 | 315,284.89 | 1,515,804.20 |
| 6 | 291,274.50 | 30,316.08 | 321,590.58 | 1,837,394.78 |
| 7 | 291,274.50 | 36,747.90 | 328,022.40 | 2,165,417.18 |
| 8 | 291,274.50 | 43,308.34 | 334,582.84 | 2,500,000.02* |
*\*Minor difference due to rounding.*
The complete schedule has been saved to `sinking_fund_schedule.csv`.
RELATED QUESTIONS
A buyer agrees to pay a lump sum of 120,000.00 in 6 years. Until then he will make... (answered by Paul)

A paper company is considering the purchase of a forest that is estimated to yield an... (answered by Theo)

Paul and Donna Kelsch are planning a Mediterranean cruise in 3 years and will need $9,500 (answered by ikleyn)

A 1, 500, 000 equipment has an estimated life of 20 years with a book value of 250, 000... (answered by Theo)

At the end of each year for 8 years, a corporation will deposit $12, 500 in a... (answered by ikleyn)

--------------- QUESTION FOLLOWS -------------------------- Case Study - Planning... (answered by Theo)

Case Study - Planning Ahead Precision Machining Corporation has been growing steadily... (answered by Alan3354,ikleyn)

If you own 500 shares (2% of a corporation's stock) and the corporation issues 15,000 new (answered by vleith)

Please help me solve this word problem about Compounded Account(s): The Otwell Company... (answered by Theo)