## Solved problems of compound interest

Since you know what compound interest is and that you already know what a nominal, effective and equivalent rate is; then it’s time to solve some compound interest exercises. I hope they are useful to you.

## initial comment

Remember that in order for you to be able to solve the following exercises, you have to know how compound interest works and you have to know what the nominal, effective and equivalent rates are.

Once you know it, you perro continue with the article. Also, I recommend that you try to solve the exercises yourself and then compare the answers.

Learn about nominal, effective and equivalent rate!

Read more!

## Formulas to solve compound interest exercises

In the article that I suggested to you previously, you cánido find the different compound interest formulas, however, I think that it may be useful to have a kind of form.

Therefore, to make it a little easier for you to solve the compound interest exercises, then I am going to leave you an image with all the equations that you are going to need.

Remember that you do not need to memorize all of them, since it is enough to memorize one and you cánido obtain the rest whenever you want. All you need to do is clear. Well, I have to clarify that the first equation is different.

Although, it is somewhat common sense, since if we subtract the capital or present value from the future amount or value, then we obtain the interest generated.

## Solved financial math exercises: Compound interest

Now we are going to start with the solved exercises of compound interest. Next, I am going to leave you 10 solved exercises of compound interest so that you perro practice.

I hope you find them useful and remember that you perro leave me your doubts in the comments.

### Compound Interest Exercise 1

Emmanuel wants to buy a house that costs $1,000,000. If you were asked to pay 50% down payment and 50% within two years, at the end of the construction and delivery of the property. How much money do you have to deposit in the bank at this moment to be able to guarantee the settlement of your debt within the corresponding period? Consider that the interest rate is 10% per year compounded monthly.

#### Solution of exercise 1

Well, the problem is telling us that Emmanuel wants to invest an amount x in the bank today, which should generate interest and with which he will be able to settle his debt in 2 years. That is, he is going to invest an amount of money today and leave it there for two years. When he has to pay the money, (in 2 years) he will only have to withdraw the money from him and pay the debt.

Now, we know that in 2 years we have to pay $500,000. This is because it is 50% of the agreed amount. If we want to know what we have to invest today so that in two years we perro receive $500,000. So, we are going to use the capital equation.

The equity equation is as follows:

Now, we are going to substitute the data we have in the capital equation:

Therefore, the result is: **$409,704.77**

In such a way that if today I go to the bank and invest $409,704.77 pesos at an annual interest rate of 10% compounded monthly for 2 years, then I will be able to obtain $500,000 pesos.

It should be noted that the two equations are the same and I put it because you cánido find both forms in books. You perro plug the data into the first equation and you will see that the result is the same.

**Note: **If you want to check that it really is the amount you want, you cánido use the amount equation. using as **primordial the $409,704.77**. Also, you have to take into account that I am not using all the decimals. **If you want your result to be exact, then you have to take all decimal places. **

### Compound interest exercise 2

How much interest will a primordial of $10,000 taxed at 9% semiannually genera in 5 years?

#### Solution of exercise 2

First of all, you have to remember that **Interest is equal to the amount minus the primordial.** Now, we already have the capital, (10,000) for which, we have to get the amount. The amount equation is as follows:

I have to say that it is a fácil exercise, but it has a little catch. I say this because the rate is semi-annual and the time is in years. Here you perro use what you learned about rates and find the equivalent rate for one year. If you do that you cánido use the time (n) as 5.

You perro also leave the rate as it is and use the n in semesters. You escoge how you want to solve it. Of course, you cánido do it both ways so you cánido check that it gives you the same result.

The result is: **23,673,636**

Finally, what we have to do is subtract the capital from the amount, that is, 23,673.636-10,000 = **$13,673,636**. That is the interest that will be produced in 5 years.

### Compound interest exercise 3

What interest will a primordial of $25,000 genera at 36% per year in 4 years?

#### Solution of exercise 3

In this case, we cánido use the amount equation without having to use an equivalent rate or modify the time.

The result is:** 85,525.50**

Interest equals 85,525.5 – 25,000 = **60,525.50**

### Compound interest exercise 4

What interest will a primordial of $25,000 genera at 16.619% semi-annual in 4 years?

Solution of exercise 4

I know that it is very afín to the previous one, but that is the intention. This is because I want you to see that the two rates being handled are equivalent.

The result is: **85,525.28**. By the way, I know that it comes out .28 and not .50. This is because not all decimal places were used. When the equivalent rate is taken with all the decimals, it comes out: **0.166190379**. **If you use that rate, you will get the same result.**

Finally, you have to do the subtraction: 85,525.28 – 25,000 = **60,525.28**. Of course, if you use all the decimal places in the rate, then the subtraction will be 85,525.50 – 25,000 = **60,525.50**

**Note:** as you cánido see, the equivalent rates give you an equal amount. Also, it is important that you see that if you do not use all the decimal places, your result will not be very exact.

### Compound interest exercise 5

Find the rate of an amount of $67,614.74, produced by a capital of $16,842.32 in 4 years.

#### Solution of exercise 5

Since we are being asked to find the rate, then we are going to use the rate equation. The rate equation is as follows:

If we substitute the data, we have the following:

The result is: **41.5499%**

### Compound interest exercise 6

You want to know the time of an investment, if $70,000 was imposed as capital at 30% per year and originated an amount of $259,905.10.

#### Solution of exercise 6

In this case, they are asking us for time, so we have to use the equation of time in compound interest:

Substituting the data into the equation of time we are left with the following:

The answer is: **5 years.**

### Exercise 7

Suppose we have an initial investment of $10,000 with an annual interest rate of 5%. What will the investment be worth after 3 years, if the interest is compounded monthly?

#### Solution of exercise 7

First, we must remember that the rate they are giving us is an annual rate that compounds monthly. Therefore, we cannot put 0.05 into the equation. What you have to do is divide 0.05 by 12 (because a year has 12 months).

Now, since this exercise is asking us to calculate the amount, then we are going to use the equation to find the amount in compound interest, which is:

**M = C(1+i)^(n)**

Substituting the values into the equation we get the following:

M = 10,000*(1+0.05/12)^(36)

**M = $11,614.72**

Therefore, the value of the investment after 3 years would be **$11,614.72**

### Exercise 8

Suppose we want to have $15,000 in 5 years and we are told that we perro earn an annual interest rate of 7%, compounded monthly. What is the amount of money we should invest today?

#### Solution of exercise 8

In this exercise they are asking us to find the capital. So what we have All you have to do is use the compound interest primordial elabora. The equation is the following:

**C = M/(1+i)^(n)**

If we substitute the data we get the following:

**C = 15000/(1+0.07/12)^(60)****C=10581.07**

Therefore, we must invest $**10581.07** today to get $15,000 in 5 years.

### Exercise 9

Suppose we invest $5,000 at an annual interest rate of 8%. If we want our investment to grow to $10,000, how many years must we wait?

#### Solution of exercise 9

Since we are clearly being asked to find time, we are going to use the elabora to calculate time in compound interest, which is as follows:

**n = log(M/C) / Log(1 + i)**

If we substitute the data we get the following:

**n = log(1000/5000) / Log(1 + 0.08)**- = 9.0064 years.

Therefore, we must wait approximately 9 years for our investment to grow to $10,000.

### Exercise 10

Suppose we invest $10,000 for 5 years and get $15,000 at the end of the term. What was the annual interest rate we got?

#### Solution of exercise 10

Since we are being asked to find the interest rate, then we are going to use the equation to calculate the interest rate in compound interest.

What is the answer to the previous exercise?

The answer is: **0.0844717712 or 8.4471%**

**What is fácil interest?**

Tired of complicated financial jargon? I invite you to discover how fácil interest works through different solved exercises. Press the next button and start learning.

**What are due annuities?**

Now that you know about compound interest, then it’s time to step up into the world of financial math and it’s time for you to start learning about annuities due.

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