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Question 1164972: A major shipping company is planning to purchase new cargo ships. It wants to borrow $1100 million by issuing bonds. The bonds are for a 15-year period with at a rate of 9 percent per year compounded quarterly. Interest is to be paid each quarter to bondholders. How much will the company have to pay in quarterly interest? How much interest will it pay over the 12-year period?
Answer by CPhill(2189)   (Show Source):
You can put this solution on YOUR website! ```python
principal = 1100 * 10**6
annual_rate = 0.09
compounding_frequency = 4
years_period = 12
quarterly_rate = annual_rate / compounding_frequency
quarterly_interest = principal * quarterly_rate
total_quarters_12_years = years_period * compounding_frequency
total_interest_12_years = quarterly_interest * total_quarters_12_years
print(f"{quarterly_interest=}")
print(f"{total_interest_12_years=}")
```
```text
quarterly_interest=24750000.0
total_interest_12_years=1188000000.0
```
To calculate the interest payments for the shipping company's bonds, we use the simple interest formula applied to each compounding period (quarter), as the interest is paid out to bondholders.
### 1. Quarterly Interest Payment
The quarterly interest rate is the annual rate divided by the number of quarters in a year.
* **Principal ():**
* **Annual Rate ():**
* **Quarters per year ():**
**The company will have to pay $24.75 million in quarterly interest.**
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### 2. Interest Paid Over a 12-Year Period
To find the total interest over 12 years, we multiply the quarterly payment by the total number of quarters in that timeframe.
* **Number of Quarters:**
**The company will pay $1,188 million (or $1.188 billion) in interest over the 12-year period.**
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