What is the Rate of Interest Charged on a 16,700 Loan if the Debt is Settled by a Payment of 20,800 at the End of 4 Years and 8 Months?

Loan calculations can be complex, especially when dealing with compounding interest. This article will guide you through the steps to calculate the rate of interest charged on a loan using the given details. We will use both the method from the HP12C calculator and the traditional simple interest approach to find the rate.

Understanding the Problem

The problem involves a loan of $16,700 which is to be repaid with a single payment of $20,800 after 4 years and 8 months. Our goal is to find the rate of interest charged over this period.

Method 1: Using the HP12C Calculator

The HP12C calculator is a powerful tool for financial calculations, especially suitable for compounding interest scenarios. Here's how you can use the HP12C to find the interest rate:

Input the loan amount as the present value (PV): -16700 Enter the future value (FV): 20800 Select the period (N): 4 years 8 months, which is 4.6667 Calculate the interest rate (I/Y).

Following these steps using the HP12C, we find that the interest rate (I/Y) is approximately 4.81% per year compounded annually.

Method 2: Using Simple Interest Calculation

Another way to approach this problem is by using the simple interest formula:

Simple Interest (SI) Future Value (FV) - Present Value (PV) 20800 - 16700 4100

The formula for simple interest is:

R SI / (PN)

Where:

SI 4100 P 16700 N 4 years 8 months, which is 4 8/12 4.6667 periods R rate of interest

Plugging in the values:

R 4100 / (16700 * 4.6667) * 12 5.26

Therefore, the rate of interest charged using simple interest is approximately 5.26%.

Method 3: Using Compound Interest Calculation

We can also solve this problem using the compound interest formula:

FV PV x (1 R)^N

Where:

FV 20800 PV 16700 N 56 months R rate of interest

Using the HP12C calculator or manual calculation, we find:

20800 / 16700 (1 R)^56

1.245508982 (1 R)^56

Take the 56th root of both sides:

R 1.245508982^(1/56) - 1 0.0039281283

Convert to percentage:

R (0.0039281283 * 12 * 100) 4.71375% compounded monthly

Therefore, the rate of interest compounded monthly is approximately 4.71375%.

Conclusion

When dealing with compounding interest, it's crucial to use the correct method to ensure accurate results. In this case, we found that the rate of interest charged on a 16,700 loan to be repaid with 20,800 after 4 years 8 months is approximately 4.81% per year compounded annually, using the HP12C calculator. The simple interest method gave us 5.26%, and the compound interest method yielded a roughly 4.71375% rate compounded monthly.

Resources

If you're looking for more tools and calculators to assist with financial calculations, the HP12C calculator is available for free in both app stores under the name Touch RPN.