Answer to Question #280805 in Financial Math for vangie

Question

find the future value and the present value of an annuity of 15,000 payable at the end of every three months for 30 payments. the first payment is due at the end of seven years. the interest rate is 11 % compounded quarterly.

Answer 1

Compute the quarterly interest rate, using the equation as shown below:

Quarterly rate

$=\frac{annual\space rate}{4}\\\frac{11\%}{4}\\=2.75$

Hence, the quarterly interest rate is 2.75%. 

Compute the present value annuity factor (PVIFA), using the equation as shown below:

$PVIFA=\frac{1−(1+Quarterly\space rate)^{−Number \space of\space payment}}{Quarterly\space rate}\\ =\frac{1−(1+0.0275)^{−29}}{2.75\%}\\=19.8061570798$

Hence, the present value annuity factor is 19.8061570798.

Compute the present value of the annuity, using the equation as shown below:

$Present \space value=\frac{Quarterly \space payment×(1+PVIFA)}{(1+Quarterly \space rate)Time}\\= \frac{15,000×(1+19.8061570798)}{(1+0.0275)^{7\space years×4}}\\=\frac{15,000×20.8061570798}{2.13742682383}\\=146,013.118539$

Hence, the present value of the annuity is 146,013.12.

Compute the future value, using the equation as shown below:

$future \space value=Present\space value×(1+Quarterly \,rate)^{Time}\\=146,013.118539×(1+0.0275)^{29+28}\\=146,013.118539×(1+0.0275)^{57}\\=146,013.118539×4.69422974668\\=685,419.124451$

Hence, the future value is 685,419.12. 

answers:

The present value of the annuity is 146,013.12

The future value is 685,419.12