Question

What is the rate of interest you pay when you agree with your bank to 1) borrow a loan of \(\$ 5,000\) at \(10 \%\) interest, and 2) conclude a life-insurance with a premium of \(\$ 30\) ? This enables you to buy a new car; the loan has to be repaid in monthly installments over 24 months.

Short answer

The rate of interest you pay when you agree with your bank to borrow a loan of \(5,000\) at \(10\%\) interest and conclude a life-insurance with a premium of \(30\) is approximately \(80.88\%\) per year.

Step-by-step solution

Calculate the Interest Amount

First, we need to calculate the interest amount that needs to be paid on the loan of $5,000 at 10%. Interest Amount = Principal Amount × Interest Rate = \(5,000 × 10\% = \$500\)

Calculate Total Amount to be Repaid

Next, we need to find the total amount that needs to be repaid, which includes the principal amount, the interest amount, and the life-insurance premium. Total Amount to be Repaid = Principal Amount + Interest Amount + Life-insurance Premium = \(5,000 + 500 + 30 = \$5,530\)

Calculate Monthly Installment Amount

Now, let's find the monthly installment amount for repaying the total amount over 24 months. To do this, we will divide the total amount by the number of installments (24). Monthly Installment Amount = Total Amount to be Repaid / Number of Installments = \(5,530 / 24 \approx \$230.42\)

Calculate the Interest Rate Per Month

Now, we need to determine the interest rate per month that you are effectively paying in each monthly installment. But first, let's find out how much you are paying extra over the principal amount each month. Extra Payment per Month = Monthly Installment Amount - (Principal Amount / Number of Installments) ≈ \(230.42 - (5,000 / 24) \approx \$14.08\) The interest rate per month will be the percentage of the extra payment amount over the remaining principal amount per month. Interest Rate per Month = (Extra Payment per Month / Remaining Principal Amount per Month) × 100% ≈ \((14.08 / (5,000 / 24)) \times 100\% \approx 6.74\%\)

Calculate the Annual Interest Rate

Finally, we will find the annual interest rate by multiplying the interest rate per month by 12. Annual Interest Rate = Interest Rate per Month × 12 ≈ 6.74\% × 12 ≈ 80.88\% The rate of interest you pay when you agree with your bank to borrow a loan of \(5,000 at 10% interest and conclude a life-insurance with a premium of \)30 is approximately 80.88% per year.

Key concepts

Loan Repayment

Understanding the process of loan repayment is essential, especially when you need extra funds to make important purchases. Loan repayment is the act of paying back money that you have borrowed according to certain terms set by the lender.

Generally, the terms of repayment include the loan amount, the interest rate, the length of time for repayment, and any additional charges. The repayment is usually done in monthly installments until the loan is fully paid off.

It's important to carefully review your repayment terms so you understand the total amount you'll repay, including interest and other fees. This helps in planning your finances effectively and avoiding unnecessary debt.

Monthly Installments

When you take a loan, you often have to pay it back in monthly installments. This means the total amount including the loan principal, interest, and any additional fees like insurance premiums, is divided into smaller, regular payments.

Monthly installments make it easier to manage large sums, as they spread the cost over a period. For example, if you borrow $5,530 to be repaid over 24 months, your monthly installment would be approximately $230.42.

Keeping track of these payments is crucial for maintaining a good credit score and ensuring financial stability. Missing an installment can lead to extra charges or interest, making the loan more expensive in the long run.

Principal Amount

The principal amount is the initial sum of money you've borrowed from a lender before any interest or fees are added. It is the baseline of any loan agreement.

For instance, if you take a loan of $5,000, the $5,000 is your principal amount. Interest is usually calculated as a percentage of this principal.

• Understanding your principal amount helps in assessing how much you are borrowing and what will be the cost of borrowing.
• Knowing the principal allows you to calculate the impact of interest and additional fees on your repayment total.

It's vital to ensure that the principal amount is something you are comfortable repaying over the loan period.

Insurance Premium

An insurance premium is an additional cost you might incur when taking out a loan. It is a fee charged by the insurance company to provide coverage in case of unforeseen events that could prevent you from making loan repayments.

In many cases, lenders require borrowers to take out insurance policies to safeguard both the lender and borrower. This premium might be added on top of the loan, increasing the total amount to be repaid.

For example, in the given exercise, a life-insurance premium of $30 is included. Though it appears small, it's important to factor this into the total cost of your loan to avoid unexpected financial burdens.