Level annuity-immediate (aₙ)

Recommended before this lesson — you can still read and practice below:

The equation of value (locked)

Problem. An loan requires payments of Rs. 8,000 at the end of each year for 5 years. With $i = 6\%$ effective, find the present value at $t=0$ .

Solution.

a_{\overline{5}|} = \frac{1 - (1.06)^{-5}}{0.06} \approx 4.2124.

PV = 8{,}000 \times 4.2124 \approx \text{Rs. } 33{,}699.

Problem. Rs. 1 deposited at the end of each year for $n$ years at rate $i$ . The accumulated value at $t=n$ is $s_{\overline{n}|} = (1+i)^n \cdot a_{\overline{n}|} = \dfrac{(1+i)^n - 1}{i}$ .

For Rs. 500/year for 4 years at 5%: $s_{\overline{4}|} = \dfrac{1.05^4 - 1}{0.05} \approx 4.3101$ , so accumulation Rs. 2,155.

Prerequisites

The annuity as a sum

Numerical use

Worked example: Loan instalment present value

Worked example: Accumulated value of an annuity-immediate

What mastery requires

Practice

Practice 1

Practice 2

Practice 3

Practice 4

Practice 5

Practice 6

Practice 7

Practice 8

Practice 9

Synthesis practice

Practice 1

Practice 2

Mastery checks