# Loan calculator

Calculate your monthly loan payments and total to pay back, depending upon the term, size of your mortgage and interest rates.

• #### Loan calculator

Calculate your monthly loan payments and total to pay back, depending upon the term, size of your mortgage and interest rates.
• Monthly loan repayment £647, Total repayment £77,677, Total interest paid £1,328

Loans are one of the most popular financial instruments as there is always a need to buy or afford something that could be hard to be done without any financial help. Moreover, for those who just consider taking a loan in some distant or near future it may seem interesting to look how much that financial help from credit institution could cost. Thus, there are many loan calculators across the Internet and it is easy to look through what conditions could be expected for the wanted amount of money. However, there is one important thing that must be mentioned. This calculator measures the monthly payments on an annuity basis. When the person takes out a loan two kinds of types of repayment can be chosen: linear or annuity. Annuity repayments main feature is that payments are the same throughout the all term of the policy, while with linear repayment the person will pay more in the beginning and less at the end of the term of the loan. Overall, the less interest is paid with linear type of repayment, however, as it costs more in the first years, more popular is the repayment on an annuity basis.

## Input

There are three main inputs that can be inserted into this calculator: the sum that wants to be borrowed, interest rate and for what amount of time the money will be borrowed. This calculator measures monthly and total payments for any sum borrowed between £500 and £100,000. Interest rate is provided to be as yearly interest rate and the amount of time is indicated to be monthly. Thus, it measures the financial obligation when the repayments are made monthly.

## Calculations

Once the inputs are inserted calculations are made. Let’s take an example where the person borrows £20,000 for 8 years with yearly interest rate of 7.2%. The calculator shows the results that the person would need to pay £275 a month and during all the term in order to repay his debt of £20,000 he will pay to the credit institution £26,368. This calculator measures the monthly payments on annuity basis. This means that throughout the repayment period he will need to pay the same amount of money each month. To calculate these monthly payments annuity formula is used:, where PV is present value of the debt or in more understanding way the amount of debt that wants to be borrowed, PMT is monthly or yearly payment, r is a monthly or yearly interest rate while t is the time period in months or years. Whether the inputs are in months or years depend from how often the repayment needs to be done. In this case all the inputs (except PV, which is an absolute number) are the monthly ones.

Let’s take a previous example, where the person borrows £20,000 for 8 years with an yearly interest rate of 7.2%. Because the payments are made monthly, all these numbers should be not on yearly basis but on monthly one. Thus, for the formula purposes £20,000 is borrowed for 8*12 =96 months with a monthly interest rate of 7.2%/12=0.6%.

Let’s insert calculations into the formula:, we can convert this formula to be: Thus, with this kind of formula we get that a monthly payment is equal to £247,67 a month and it is a bit more correct answer than the one provided by the calculator as the calculator rounds the answer. However, the difference is not high and rounded number is easier to understand.

After the monthly payment calculation is done, it is easy to calculate total amount of money that will be paid to the financial institution. The monthly payment is multiplied by the number of months. In our case, £275 (the answer provided by the calculator) is multiplied by 96. If someone would want to calculate this by himself he would get that £275 * 96 = £26,400, which is not the same as the sum £26,368, which is provided by the calculator. It is this way because even though when showing monthly repayment the calculator rounds it for £275, for the calculation of the total repayment not rounded monthly payment (~£247.67) is used to calculate the total amount of money that will be needed to pay for the creditor. Thus, by using not rounded calculation, more correct answer for total repayment is given. However, the difference is very small while calculation process is easier.