# Loan with equal annual repayments

• nokia8650
In summary, the problem involves a man who takes out a 5 year loan for $10,000 with an annual interest rate of 8%. The task is to determine the amount that must be paid each year, given that the annual repayments are equal. To solve this, the borrower needs to use algebra to calculate the interest and remaining amount owed after each annual payment. By setting the remaining amount owed after the fifth payment to 0 and solving for P, the annual payment amount can be determined. nokia8650 I was undertaking the following problem: A man takes out a 5 year loan for$10,000 with an annual interest of 8% with equal annual repayments. How much must be paid each year?

I'm stuck as to where and how to start. Is there are particular equation which I should be using?

Thanks

The first time you posted this, it was deleted because you had not shown any work. Now you have reposted, still showing no work!

Last edited by a moderator:
Sorry, I really don't know where to start; would it be possible for you to give me a nudge in the right direction so that i can work it through?

Well, how about just doing the algebra? He borrowed $10000 at 8% interest so his interest for the first year is (.08)(10000)=$800. At the end of the first year he owes \$10800. If his annual payment is P, after that payment, he still owes 10800- P.

How much will the interest be for the second year? Add that to the 10800-P he owed to get how much he owes before his payment. How much will he owe after his annual payment?

Now do that for the third, fourth, and fifth years. Set the amount still owed after his fifth annual payment to 0 and solve for P.

## 1. What is a loan with equal annual repayments?

A loan with equal annual repayments is a type of loan where the borrower agrees to pay back the borrowed amount, along with interest, in a series of equal payments over a set period of time. The amount of each payment remains the same throughout the duration of the loan.

## 2. How does a loan with equal annual repayments work?

A loan with equal annual repayments works by dividing the total amount borrowed, plus interest, into equal payments that are spread out over a set period of time. Each payment includes a portion of the principal amount borrowed as well as the accrued interest.

## 3. What are the benefits of a loan with equal annual repayments?

One benefit of a loan with equal annual repayments is that it allows for predictable and manageable payments. Borrowers know exactly how much they need to pay each year, making budgeting easier. Additionally, with equal payments, borrowers can gradually pay off the loan without being burdened by a large lump sum payment at the end.

## 4. Are there any disadvantages to a loan with equal annual repayments?

One potential disadvantage of a loan with equal annual repayments is that it may have a higher interest rate compared to other types of loans. This is because the lender is assuming more risk by spreading out the payments over a longer period of time. Additionally, borrowers may end up paying more in total interest over the life of the loan compared to other payment structures.

## 5. How do I know if a loan with equal annual repayments is right for me?

The decision to take out a loan with equal annual repayments should be based on your individual financial situation and needs. Consider factors such as your income, expenses, and other debts before deciding if this type of loan is the best option for you. It may also be helpful to consult with a financial advisor for personalized advice.

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