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What’s it: Annuity is a way of payment or receipt periodically over a certain period. Various financial products use this concept, for example, insurance policies, pension fund benefits, and bank loan interest.
For example, in insurance, you pay the premium to the insurance company. In return, you receive regular payments for an agreed period of time or during your retirement.
Why are annuities important
Having regular income in retirement is the dream of many people. And, annuity products appear to fulfill that desire.
When you buy them right, annuities provide regular income in retirement. You give the insurance company money upfront. In exchange, you get a steady income, for example, each month, at retirement. You will continue to receive fixed payments and whatever happens in the market (except the company goes bankrupt).
How an annuity works
In an annuity, you receive or make regular payments. It can be monthly, quarterly, or annually. You can accept it or give it at the beginning or end of the payment period, which value may be fixed or variable. Some annuity payments are also linked to an index, for example, the S&P 500 equity index.
Types of annuity
In this article, I focus on the types of annuities based on the payment period. In general, it falls into two categories:
- Ordinary annuity: payment or receipt occurs at the end of a period
- Annuity due: payment or receipt is made at the beginning of the period.
Here is the annuity formula:
Let’s take an example of calculating bank loan installments using the annuity method. For example, suppose you borrowed money from the bank amounting to IDR1,000 for one year. It charges an annual interest rate of 12% and requires monthly installments. Assume that the loan is an ordinary annuity.
Applying the formula above, you calculate the installment amount per month as follows:
Installments per month = 1% * 1,000 / ((1- (1 + 1%) ^ (- 1 * 12))) = IDR88.5
In this calculation, you must convert the interest rate. Since the installment payments are monthly, you should use the monthly interest rate and convert the annual interest rate above to 12%/12 = 1%.
Furthermore, you can also more easily calculate annuities using Excel. Microsoft Excel has provided several functions to do this.
This time, I will discuss three main functions in Excel. You can use the PMT function for calculating installments, IPMT for calculating interest payments, and PPMT for principal installments.
Here is an example of calculating the annuity using Excel:
To calculate in Excel, you need to input the following variables:
- Rate: interest per period. In the above case, the interest rate is 1%.
- nper: number of payment or receipt periods. Since you apply for an annual loan and pay each month, the number payment period is 12 months = 1 year.
- pv: principal amount. Do the example above, it is IDR1,000.
- fv: the principal amount at the end of the loan period. Since the loan has been paid off, the value is Rp0.
- type: type of annuity. A value of 0 is for ordinary annuity and 1 for an annuity due.
- per: installment period. For the first month’s installment, you enter 1. For the second installment, that means 2, and so on. To make calculations easier in Excel, write down the installment period in a separate column, namely the month column, as shown above.
For example, for the first and second months, the numbers you should enter are as follows:
| 1st month | 2nd month | |
| Installment | =PMT(1%,12,1000,0,0) | =PMT(1%,12,1000,0,0) |
| Interest | =IPMT(1%,1,12,1000,0,0) | =IPMT(1%,2,12,1000,0,0) |
| Principal | =PPMT(1%,1,12,1000,0,0) | =PPMT(1%,2,12,1000,0,0) |
| Balance | = 1.000-78,85 | = 1.000-78,85 |
Difference between annuity and bond coupons
Although both pay periodically, the concept of bond coupon payment is different from annuities. Annuity consists of two components, namely principal and interest. Take a bank loan as the previous example. When paying installments, you are basically paying a portion of the principal and the interest.
The proportion of interest to total installments is relatively high at the beginning of the installment. It then decreases toward maturity. See the example above. In the first month, you pay interest of IDR10 or around 11.3% of the total installment. Meanwhile, around 88.7% of your installments are for principal payments (IDR78.95). The percentage of interest decreases and becomes only 2.0% in the 11th month (IDR1.75).
For this reason, many people suggest that we do not need to pay installments that exceed a predetermined amount of installments. This is because we actually only pay the loan interest, not the principal. Thus, the next installment will still be large because the principal is only slightly reduced.
Meanwhile, in bonds, the bond issuer pays regular (coupon) interest every quarter or semester. The payment does not include principal installments. At the end of maturity, the issuer repays all of the principal on loan.
For example, suppose a company issues an IDR1,000 bond with a 2% coupon per quarter. In this case, the company pays a regular coupon of IDR20 (2% x IDR1,000) per quarter. And at maturity, the company will pay off the principal amounting to IDR1,000.
