The Basics of Compound Interest

Oct 13, 2025 by miodeya.com 58 views

Introduction

Compound interest is a powerful financial concept that can help individuals grow their savings over time. However, it can also work against them if they're not careful. In this article, we'll explore how compound interest works and how monthly payments can impact the total amount owed on a loan.

The Basics of Compound Interest

Compound interest is the interest earned on both the principal amount and any accrued interest over time. It's calculated using the formula:

A = P(1 + r/n)^(nt)

Where:

A is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
r is the annual interest rate (in decimal form).
n is the number of times that interest is compounded per year.
t is the time the money is invested or borrowed for, in years.

The Problem

Suppose you borrow $\$3700$ at a $21\%$ annual interest rate, compounded monthly ( $1.75\%$ each month). At the end of each month, you make a $\$200$ payment. We'll use this information to complete the table below.

Month	Beginning Balance	Interest	Payment	Ending Balance
1	3700.00	63.75	200.00	3563.75
2	3563.75	61.88	200.00	3424.63
3	3424.63	60.04	200.00	3284.67
4	3284.67	58.22	200.00	3146.89
5	3146.89	56.41	200.00	3002.30
6	3002.30	54.64	200.00	2856.94
7	2856.94	52.90	200.00	2716.84
8	2716.84	51.19	200.00	2576.03
9	2576.03	49.51	200.00	2435.54
10	2435.54	47.86	200.00	2296.40
11	2296.40	46.24	200.00	2156.64
12	2156.64	44.65	200.00	2016.29
13	2016.29	43.10	200.00	1873.39
14	1873.39	41.57	200.00	1732.96
15	1732.96	40.07	200.00	1592.03
16	1592.03	38.60	200.00	1449.63
17	1449.63	37.16	200.00	1306.79
18	1306.79	35.75	200.00	1166.54
19	1166.54	34.37	200.00	1026.91
20	1026.91	32.99	200.00	888.90
21	888.90	31.64	200.00	751.54
22	751.54	30.31	200.00	621.85
23	621.85	28.99	200.00	509.84
24	509.84	27.69	200.00	437.53
25	437.53	26.41	200.00	373.94
26	373.94	25.15	200.00	318.09
27	318.09	23.90	200.00	271.99
28	271.99	22.67	200.00	233.66
29	233.66	21.46	200.00	204.12
30	204.12	20.27	200.00	184.39

Calculating the Ending Balance

To calculate the ending balance for each month, we'll use the formula:

Ending Balance = Beginning Balance + Interest - Payment

Where:

Beginning Balance is the balance at the beginning of the month.
Interest is the interest earned on the principal amount for the month.
Payment is the payment made at the end of the month.

Analyzing the Results

From the table above, we can see that the ending balance decreases each month as the payment is made. However, the interest earned on the principal amount increases each month, which means that the total amount owed on the loan increases over time.

Conclusion

In this article, we've explored how compound interest works and how monthly payments can impact the total amount owed on a loan. We've used a table to calculate the ending balance for each month, taking into account the interest earned on the principal amount and the payment made at the end of each month.

Key Takeaways

Compound interest can work against individuals if they're not careful.
Monthly payments can help reduce the total amount owed on a loan.
The interest earned on the principal amount increases each month, which means that the total amount owed on the loan increases over time.

References

Compound Interest Formula
Monthly Payment Formula
Compound Interest and Monthly Payments: A Q&A Guide =====================================================

Introduction

In our previous article, we explored how compound interest works and how monthly payments can impact the total amount owed on a loan. In this article, we'll answer some of the most frequently asked questions about compound interest and monthly payments.

Q: What is compound interest?

A: Compound interest is the interest earned on both the principal amount and any accrued interest over time. It's calculated using the formula:

A = P(1 + r/n)^(nt)

Where:

A is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
r is the annual interest rate (in decimal form).
n is the number of times that interest is compounded per year.
t is the time the money is invested or borrowed for, in years.

Q: How does monthly payment impact compound interest?

A: Monthly payments can help reduce the total amount owed on a loan by paying off the principal amount and interest. However, the interest earned on the principal amount increases each month, which means that the total amount owed on the loan increases over time.

Q: What is the difference between simple interest and compound interest?

A: Simple interest is the interest earned only on the principal amount, while compound interest is the interest earned on both the principal amount and any accrued interest over time.

Q: How can I calculate the monthly payment for a loan?

A: You can use a monthly payment calculator or the formula:

M = P[r(1 + r)^n]/[(1 + r)^n – 1]

Where:

M is the monthly payment.
P is the principal amount.
r is the monthly interest rate.
n is the number of payments.

Q: What is the impact of interest rate on compound interest?

A: The interest rate has a significant impact on compound interest. A higher interest rate means that the interest earned on the principal amount increases, which means that the total amount owed on the loan increases over time.

Q: Can I use a compound interest calculator to calculate the ending balance?

A: Yes, you can use a compound interest calculator to calculate the ending balance. Simply enter the principal amount, interest rate, and number of payments, and the calculator will give you the ending balance.

Q: What is the impact of payment frequency on compound interest?

A: The payment frequency has a significant impact on compound interest. Making payments more frequently can help reduce the total amount owed on the loan by paying off the principal amount and interest.

Q: Can I use a monthly payment calculator to calculate the total amount owed on a loan?

A: Yes, you can use a monthly payment calculator to calculate the total amount owed on a loan. Simply enter the principal amount, interest rate, and number of payments, and the calculator will give you the total amount owed.

Q: What is the impact of inflation on compound interest?

A: Inflation can have a significant impact on compound interest. As inflation increases, the purchasing power of money decreases, which means that the interest earned on the principal amount decreases.

Q: Can I use a compound interest calculator to calculate the future value of an investment?

A: Yes, you can use a compound interest calculator to calculate the future value of an investment. Simply enter the principal amount, interest rate, and number of years, and the calculator will give you the future value of the investment.

Conclusion

In this article, we've answered some of the most frequently asked questions about compound interest and monthly payments. We've also provided some tips and resources to help you calculate the ending balance, monthly payment, and total amount owed on a loan.

Key Takeaways

Compound interest can work against individuals if they're not careful.
Monthly payments can help reduce the total amount owed on a loan.
The interest rate has a significant impact on compound interest.
The payment frequency has a significant impact on compound interest.
Inflation can have a significant impact on compound interest.