### Annuity Loan Calculator

Here is a calculator to calculate annuity loans and what you have to pay per term on such a loan. The calculator correctly calculates the effective interest rate.

What characterizes an annuity loan is that the amount of interest and installments (the installment amount) is constant throughout the period.

## You first enter the loan amount The calculator calculates the effective interest rate, total interest and fee, as well as what installment amount you have to pay. A repayment plan is calculated for up to the first 12 installments, and the annual sums for all the years.
If the loan is to be repayable, the installment amount will correspond to the column for interest and fees in the first installment.

## Annuity loans mean that you repay the loan with equal installments until the loan is repaid Initially, the installment portion is small, while the interest portion is large. As time goes on, the installment portion rises and the interest portion decreases. So the sum is constant.

With a serial loan, you pay the same installment every term (usually every month). Interest rates are highest when the repayment starts and falls gradually as the loan decreases. The total amount paid (the installment amount) will thus fall from month to month.

### Example of an annuity loan scenario: For the following scenario, help is needed.

Annuity loans, large SEK 250,000.-
Maturity, 20 years
Nominal interest rate 7, 8%
No fees except
Monthly payment

Q1: How is the effective interest rate calculated?
Q2: How is the monthly total amount (interest and installments) calculated?
Q3: Also wants a repayment plan that specifies interest and installments month by month until the entire loan is paid off.

1. Effective interest rate = nominal interest rate when there is no installment and monthly interest rate =
100 * ((1 + p / 100) ^ (1/12) -1) and p is annual interest.

2. S = 250000, q = (1 + 7.8 / 100) ^ (1/12) ^, N = 12 * 20
Monthly payment = S * q ^ N * (q-1) / (q ^ N-1)

3. Payments in month n after borrowing: S * q ^ (n-1) * (q-1) / (q ^ N-1)
Interest in month n: Monthly payment – Installment in month.