Download presentation

Presentation is loading. Please wait.

Published byDelilah Palmer Modified over 9 years ago

1
Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use 1 Present Value of an Annuity Stage 6 - Year 12 General Mathematic (HSC)

2
22 Present Value of Annuity (1/6) This is the single amount of money which invested, as compound interest, under the same terms as the annuity that will produce the same financial result. N = A (1+r) n A A is the future value of the investment. N N is the present value of an annuity. r r is the rate of interest per period as a decimal. n n is the number of periods.

3
33 Present Value of Annuity (2/6) Mary has an annuity that has a Future Value of $200 000 on her retirement in 30 years. The annuity is invested at 4.5% compounding annually. Calculate the NPV. N = 200 000 (1+0.045) 30 = 200 000 1.045 30 = $53 400.00 N = A (1+r) n

4
44 Present Value of Annuity (3/6) Mary has an annuity that has a Future Value of $200 000 on her retirement in 30 years. The annuity is invested at 4.5% compounding annually. Calculate the NPV. P = N = $53 400.00 A = P (1 + r) n A = 53 400 (1 + 0.045) 30 A ≈ $ 1 999 999.99 = 53 400 x 1.045 30

5
55 Present Value of Annuity (4/6) This is the single amount of money which invested, as compound interest, under the same terms as the annuity that will produce the same financial result. N =M (1+r) n -1 r(1+r) n M M is the amount of the equal periodical investments. N N is the present value of an annuity. r r is the rate of interest per period as a decimal. n n is the number of periods. { }

6
6 6 Present Value of Annuity (5/6) N =M (1+r) n -1 r(1+r) n { } Mark has an annuity that has annual deposits of $2 000 for his retirement in 30 years. The annuity is invested at 4.5% compounding annually. Calculate the NPV. N = 2000 (1+0.045) 30 -1 0.045(1+0.045) 30 = 2000 x (1.045 30 -1) (0.045x1.045 30 ) = $32 577.78

7
77 Present Value of Annuity (6/6) Mark has an annuity that has annual deposits of $20 000 for his retirement in 30 years. The annuity is invested at 4.5% compounding annually. Calculate the NPV. N = P = $32 577.78 A = P (1 + r) n A = 32 577.78 (1 + 0.045) 30 ≈ $ 122 014.15 = 32 577.78 x 1.045 30 { } A = MA = M (1+r) n -1 r { } A = 2000 (1 + 0.045) 30 - 1 0.045 = 2000 x (1.045 30 - 1) 0.045 = $122 014.14 Future Value of the Annuity

Similar presentations

© 2024 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google