Answer to Question #181974 in Financial Math for Anamika

Question

11.A man makes payments into an investment account of $300 at time 5, $280 at time 6, $260 at time 7, and so on until a payment of $180. Assuming an annual effective rate of interest of 4.25%, calculate

PV of the payments at time 3

PV of the payments at time 0

AV of the payments at time 11

12.Calculate the PV of an annuity at year 2 where the first payment is Rs. 700 at the beginning of year 4 and then keeps increasing by Rs. 75 every year thereafter till year 18. At a rate of interest of 3.62% p.a. compounded 4-monthly. Also calculate the AV at year 21.

Answer 1

11.You can see that 5-7 years differ by the same difference. Therefore, you can find the remaining years with this difference taken into account

0 -400

1 - 380

2-360

3-340

4-320

5-300

6-280

7-260

8-240

9-220

10-200

11-180

find the nominal interest rate

$i=(1+\frac{r}{m})^m-1$

$4.25=(1+\frac{r}{1})^1-1$

$4.25=(1+\frac{r}{1})^1-1$

r=4.25

$PV3=PMT\frac{1-\frac{1}{(1+r)^n}}{r}$

$PV3=340\frac{1-\frac{1}{(1+0.0425)^3}}{0.0425}=939.07$

$PV0=400\frac{1-\frac{1}{(1+0.0425)^0}}{0.0425}=0$

$FV11=180\frac{(1+0.0425)^{11}-1}{0.0425}=2459.24$

12.700 at the beginning of year 4 and then keeps increasing by Rs. 75 every year 

4-700

5-775

6-850

7 -925

....

21 = 1975

$r=\frac{0.0362}{3}=0.012067$

n=6

$2\times3=6$

$PV6=850\frac{1-\frac{1}{(1+0.0120607)^6}}{0.0120607}=4882.32$

n=51

$17\times3=51$

$FV21=1975\frac{(1+0.0120607)^{51}-1}{0.0120607}=140126.40$