Konsep Anuitas Dalam Time Value of Money | Dr. Hj. Datien Eriska Utami, SE., M.Si

Main Ideas

Time Value of Money

The time value of money has four calculation methods:

1. Future value (FV)
2. Present value (PV)
3. Present value of an annuity (PVA)
4. Future value of an annuity (FVA)

An annuity is a series of equal payments or receipts made at regular intervals. The examples in the lecture use payments made at the end of each period.

Present Value of an Annuity

PVA calculates what a series of future payments is worth today. Each payment is discounted separately, and the present values are added together.

Formula:

PVA = PMT × [1 − (1 + i)⁻ⁿ] / i

Where:

• PMT = payment per period
• i = interest or discount rate per period
• n = number of periods

The factor [1 − (1 + i)⁻ⁿ] / i is known as the present value interest factor for an annuity (PVIFA).

Example: Receiving Rp8,000 at the end of each year for 3 years, discounted at 8%, has a present value of about Rp20,616. It is not simply Rp24,000 because payments received later are worth less today.

Future Value of an Annuity

FVA calculates the value at a future date of a series of periodic payments. Earlier payments earn interest for longer.

Formula:

FVA = PMT × [(1 + i)ⁿ − 1] / i

The factor [(1 + i)ⁿ − 1] / i is the future value interest factor for an annuity (FVIFA).

Example: Depositing Rp100,000 at the end of each year for 4 years at 10% produces a future value of about Rp464,100 at the end of year 4.

Application: Loan Amortization

Loan amortization is the repayment of a loan through equal payments over a specified period.

To determine the periodic installment, the loan amount, interest rate, and repayment term are entered into the present value of an annuity formula. Each payment is divided between:

• Interest on the outstanding balance
• Principal repayment, which reduces the balance

A loan amortization schedule records the payment, interest, principal repaid, and remaining balance for each period.

Example: A company borrows Rp1 billion and repays it over 3 years at 6%. The lecture gives an installment of about Rp374.11 million per period. The same approach is used in lending, including housing loans.

Speakers and Sources

• Dr. Hj. Datien Eriska Utami — lecturer in the Sharia Business Management Study Program at UIN Raden Mas Said Surakarta. The auto-generated subtitles render her name as “Dandin Eriska Utami.”
• FEBI TV — the video’s channel and source.