Annuity-due (äₙ) and p-thly annuities

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

Level annuity-immediate (aₙ) (locked)

Problem. Rent of Rs. 12,000 is paid at the start of each year for 3 years. With $i = 5\%$ effective, find the present value at $t=0$ .

Solution.

a_{\overline{3}|} = \frac{1 - 1.05^{-3}}{0.05} \approx 2.7232, \qquad \ddot{a}_{\overline{3}|} = 1.05 \times 2.7232 \approx 2.8594.

PV = 12{,}000 \times 2.8594 \approx \text{Rs. } 34{,}313.

Problem. Rs. 1 per year for 4 years at $i=4\%$ . Find $a_{\overline{4}|}$ and $\ddot{a}_{\overline{4}|}$ (three decimals).

Solution. $a_{\overline{4}|} = (1 - 1.04^{-4})/0.04 \approx 3.630$ . .

Prerequisites

Annuity-due vs annuity-immediate

Worked example: Rent paid in advance

p-thly annuities

Worked example: Due vs immediate difference

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

Annuity-due (äₙ) and p-thly annuities — skill 1

Check 1

Check 2

Check 3

Annuity-due (äₙ) and p-thly annuities — skill 2

Check 1(Complete prior skills first)

Check 2(Complete prior skills first)

Check 3(Complete prior skills first)

Annuity-due (äₙ) and p-thly annuities — skill 3

Check 1(Complete prior skills first)

Check 2(Complete prior skills first)

Check 3(Complete prior skills first)

Unlock the full Theory of Interest Rates module

Prerequisites

Teach

Annuity-due vs annuity-immediate

Worked example: Rent paid in advance

p-thly annuities

Worked example: Due vs immediate difference

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

Annuity-due (äₙ) and p-thly annuities — skill 1

Check 1

Check 2

Check 3

Annuity-due (äₙ) and p-thly annuities — skill 2

Check 1(Complete prior skills first)

Check 2(Complete prior skills first)

Check 3(Complete prior skills first)

Annuity-due (äₙ) and p-thly annuities — skill 3

Check 1(Complete prior skills first)

Check 2(Complete prior skills first)

Check 3(Complete prior skills first)

Unlock the full Theory of Interest Rates module