Question

Aditya has an annuity of 28 annual payments of $200 each. The annual interest rate is 6%. Which of the following valuations is incorrect? If it is an annuity due, its present value is $2841.11 If it is an annuity due, its future value is $14527.96 If it is an annuity immediate, its present value is $2781.23 If it is an annuity immediate, its future value is $13705.62. Show your formula by hand to show your understanding.

Answer 1

Present value P+Px[1-(1:(1+r)^(n-1)]=r Here, 6% 28 m 1 Interest rate per annum 2 Number of years 3 Number of compoundings per per annum = 1-3 Interest rate per period (r) = 2x3 Number of periods (n) Payment per period (P) 1 6% 28 200 $ Present value $ 2,842.11 200+200x(1-(1:(1+6%)^(28-1))):6%

Future value (1+r)xPx[(1+r)^n-1]=r Here, A Interest rate per annum B Number of years Number of compoundings per per annum A:C Interest rate per period (r) BxC Number of periods (n) Payment per period (P) 6% 28 1 6% 28 $ 200 Future value $ 14,527.96 (1+6%)x200x((1+6%)^28-1):6%

Hence correct option is " its future value is $14527.96".

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