Answer to Question #193964 in Financial Math for King

Question

PV of annuity due

5) find the present value of annuity due of 7,000 payable at the beginning of each quarter for six years if the interest rate is 14% compounded quarterly.

6) what is the cash prize of a freezer than can be bought for 7500 a quarter for 2&1/2 if the interest payment is made now and the interest rate is 7%compounded quarterly?

Answer 1

5.)

Annuity Due refers to series of equalized payments that are made at START of definite interval for finite time period.

Compute Present Value(PV) as below:

Resultant table:

Hence, PV is $116,342.87

6.)

GIVEN,

A= 7500

N = 2.5

R=7%

M = 4 ( QUARTERLY PAYMENT)

$PV=A\times(\frac{1-(1+\frac{R}{M})^{-M\times N}}{\frac{R}{M}})$

$=7500\times(\frac{1-(1+\frac{0.07}{4})^{-4\times 2.5}}{\frac{0.07}{4}})$

$=7500\times9.10\\=68,259.17$

 ANSWER: 68,259.17