**Future Value of a Single Amount Problems and Solutions**

**Problem 1: **

Calculate simple interest and compound interest assuming that principal amount is Rs. 10,000; interest rate is 9% for three years. What is the amount different between compound and simple interest?

**Solution: **

**Difference = 2,950.29 – 2,700 = Rs. 250.29**

**Problem 2:**

You are scheduled to receive Rs. 13,000 in two years. When you receive it, you will invest it for six more years at 8 percent per year. How much will you have in eight years?

**Solution: **

13,000 (1 + 0.08) ^{6}

**Answer: Rs. 20,629.37**

**Problem 3:**

You have Rs. 9,000 to deposit. ABC Bank offers 12 percent per year compounded monthly, while King Bank offers 12 percent but will only compound annually. How much will your investment be worth in 10 years at each bank?

**Solution: **

ABC Bank

9,000 (1 + 0.12/12) ^{10 * 12}

**Answer: Rs. 29,703.48**

King Bank

9,000 (1 + 0.12) ^{10 }

**Answer: Rs. 27,952.63**

**Variance Rs. 1,750.85**

**Problem 4:**

You invest Rs. 10,000. During the first year the investment earned 20% for the year. During the second year, you earned only 4% for that year. How much is your original deposit worth at the end of the two years?

**Solution: **

FV =10,000 (1.20) (1.04)

**Answer: Rs. 12,480**

**Problem 5:**

Ali deposited Rs. 2,500 in an account that pays 6% simple interest. How much money will he have at the end of 3 years?

**Solution: **

2,500 + (2,500 * 0.06 * 3)

**Answer: Rs. 2,950**

**Problem 6:**

What is the future value of Rs. 26 invested for 32 years at an average rate of return of 7%?

**Solution: **

FV = 26 (1.07) ^{32}

**Answer: Rs. 226.60**

**Problem 7:**

If interest is compounded quarterly, how much will you have in a bank account?

**(a)** If you deposit today Rs. 8,000 at the end of 3 months, if the bank pays 5.0% APR?

**Solution (a): **

8,000 (1 **+** 0.05 / 4)

**Answer: Rs. 8,100**

**(b)** If you deposit today Rs. 10,000 at the end of 6 months, if the bank pays 9.0% APR?

**Solution (b):**

10,000 (1 **+** 0.09 / 4) ^{2}

** Answer: Rs. 10,455.06**

**(c)** If you deposit today Rs. 80,000 at the end of 12 months, if the bank pays 8.0% APR?

**Solution (c):**** **

80,000 (1 **+** 0.08 / 4) ^{1 * }^{4}

** Answer: Rs. 86,594.57**

**(d) **If you deposit today Rs. 5,000 at the end of 24 months, if the bank pays 5.0% APR and compound monthly?

**Solution (d):**** **

5,000 (1 **+** 0.05 / 4) ^{2 * }^{4}

** Answer: Rs. 5,522.43**

**Problem 8:**

Find the future value of Rs. 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.

**Solution: **

FV = 100,000 (1.06)^{5}(1.065)^{5}(1.075)^{5}

FV = 100,000 (1.3382) (1.37009) (1.43563)

FV = 100,000 (2.6322)

**Answer: Rs. 263,220**

**Problem 9:**

The Green Corporation needs Rs. 50 million to repay a loan which is due at the end of seven years. If Green makes the following sinking fund payments, will there be sufficient funds available to repay the loan on schedule?

**Solution: **

FV of the Rs. 12 million = 12(1.11)^{7} = Rs. 24.9139

FV of the Rs. 10 million = 10 (1.1)^{5} = Rs. 16.1051

FV of the Rs. 8 million = 8(1.09)^{3} = Rs. 10.3602

**Answer: Rs. 51.382 Million**

**Problem 10:**

If farm land is currently worth Rs. 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?

**Solution: **

5 years: Rs. 1,750 * 1.2763

**Answer: Rs. 2,233.53**

10 years: Rs. 1,750 * 1.6289

**Answer: Rs. 2,850.58**

20 years: Rs. 1,750 * 2.6533

**Answer: Rs. 4,643.28**