Question

Problem 16

Find the future value of 100,000 for 15 years. The current five-year rate is 6%. Rates for the second and third five-year periods and expected to be 6.5% and 7.5%, respectively.

The answer is:

Problem 17

If farm land is currently worth 1,750 per acre and is expected to increase in value at a rate of 5 percent annually, what will it be worth in 5 years? In 10 years? In 20 years by factor formula and table?

The answer is:

Answer 1

1) Future value of 100,000 for 15 years

The rates are as follows :

First 5 years = 6%

6th year to 10th year = 6.5%

11th year to 15th year = 7.5%

Future Value = Amount x (1 + r ) ^ n

Where r = rate of interest and n = no. of years

i) On the fifth year, the investor will receive : 100,000 x (1+0.06)^5 = 1,33,822.56

ii) On the tenth year, the investor will receive : 1,33,822.56 x (1+0.065)^5 = 1,83,348.5

iii) On the fifteenth year, the investor will receive : 1,83,348.5 x (1+0.075)^5 = 2,63,220.48

The future value will be 2,63,220.48

2) Farm land value :

Current rate = 1,750/ acre

Expected rate of increase in value = 5% per annum

Future value = Amount x (1 + r ) ^ n

Where r = rate of interest and n = no. of years

The value of (1+r)^n can be referred from Future value table. The factor is then multiplied with the amount (1,750)

1) Value in 5 years = 1,750 x 1.2763 = 2,233.525

2) Value in 10 years = 1,750 x 1.6289 = 2,850.58

3) Value in 20 years = 1,750 x 2.6533 = 4,643.28

(to refer the factor, check the no. corressponding to the rate and the period. For instance, refer the 5% column in the table and 5 years row for the 1st part, 10 years row for the second part and 20years row for the third part)