Question

Annuity what is the present value of an annuity that consists of 20 semiannual payments of $1000 at an interest rate of 9% per year, compounded semiannually?

Answer 1

The present value of an annuity that consists of 20 semiannual payments of $1000 at compound interest is $  13,022.

Compound interest, or 'hobby on hobby', is calculated using the compound hobby formulation. The formula for compound interest is A = P(1 + r/n)^nt, in which P is the foremost balance, r is the hobby rate, n is the number of instances hobby is compounded consistent with term and t is the number of time intervals.

P = principa anount

R = rate of interest

P = R ( 1 - $\frac{1}{(1=R)^n}$/r

R = 1000

r = 0.09/2 = 0.045

n = 20

P = 1000 (  1 - (1.045)^-20)/0.045

   = 1000 (1- 0.414)/0.045

    = 1000* 0.586/0.045

     = 1000 * 0.586/0.045

   = 13,022.2

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Answer 2

Amount after 20 semiannual of $1000 at compound interest is $  13,022.

Compound hobby is the addition of hobby to the important sum of a loan or deposit, or in other phrases, hobby on essential plus hobby.

Let p is principal interest

  R is rate of interest

 r is the time interval

P = R ( 1 - /r)

R = 1000

r = 0.09/2 = 0.045

time interval (n) = 20

P = 1000 (  1 - (1.045)^-20)/0.045

⇒1000 (1- 0.414)/0.045

 ⇒1000* 0.586/0.045

  ⇒1000 * 0.586/0.045

  ⇒$13,022

Hence the amount is = $13,022.

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