Question

An ordinary annuity selling at $3,806.77 today promises to make equal payments at the end of each year for the next six years (N). If the annuity’s appropriate interest rate (I) remains at 5.00% during this time, the annual annuity payment (PMT) will be .

Answer 1

Answer:

• The annual annuity payment (PMT) will be $750.00

Explanation:

The value of a annuity payment, A, is equal to the present value of the future payments.

When the interest rate,r, and the annual annuity payment (PMT) remain constant over the entire life of the annuity, the formula for the value of the annuity is:

      $A=PMT\times \bigg[\dfrac{1}{r}-\dfrac{1}{r(1+r)^{t}}\bigg]$

To caculate PMT substitute:

• A = $3,806.77
• r = 5.00% = 0.05
• t = 6 years

      $\ 3,806.77=PMT\times \bigg[\dfrac{1}{0.05}-\dfrac{1}{0.05(1+0.05)^{6}}\bigg]$

Compute and solve for PMT:

             $\ 3,806.77=PMT\times \bigg[20-14.9243079\bigg]\\\\\\PMT=\ 3,806.77/5.07569207=\ 750.00$