1 You have 1000 to invest for five years How much additional

1) You have $1,000 to invest for five years. How much additional interest will you earn if the investment provides a 5% annual return, when compared to a 4.5% annual return? 2) Suppose you need $15,000 in 3 years. If you can earn 6% annually, how much do you need to invest today? 3) At 5 percent interest, how long does it take to double your money? 4) Assume that in January 2016, the average house price in a particular area was $276,400. In January 2010, the average price was $193,300. What was the annual increase in selling price? You decide to deposit $2500 in a bank for 4 years. Chase provides 5% compound interest rate while Citi offers 6% simple interest rate, which bank will you prefer and why? 5)

Solution

Question 1

This question requires application of basic time value of money function: FV = PV * (1 + r)ⁿ

At 4.5% interest rate,

FV = 1000 * (1 + 4.5%)⁵ = 1000 * 1.246182 = $1,246.18. Therefore, interest = $1,246.18 - $1,000 = $246.18

At 5% interest rate,

FV = 1000 * (1 + 5%)⁵ = 1000 * 1.276282 = $1,276.28. Therefore, interest = $1,276.28 - $1,000 = $276.28

Additional Interest = $276.28 - $246.18 = $30.10

Question 2

Again, we would use the same TVM function: FV = PV * (1 + r)ⁿ

15000 = PV * (1 + 6%)³

PV = 15000/(1 + 6%)³

PV = 15000/1.1910

PV = $12,594.29

Question 3

We will again use the same TVM function: FV = PV * (1 + r)ⁿ

You want to double the amount you invested today:

2PV = PV * (1 + 0.05)ⁿ

2 = (1.05)ⁿ

Taking natural log on both sides,

LN (2) = n LN(1.05)

n = LN(2)/LN(1.05) = 0.6931/0.0488 = 14.21 years

Question 4

This question also requires application of basic TVM function: FV = PV * (1 + r)ⁿ

276,400 = 193,300 * (1 + r)⁶

1.4299 = (1 + r)⁶

1 + r = 1.0614

r = 6.14%

Question 5

Mathematical formula for Compound interest is: FV = PV * (1 + r)ⁿ

Mathematical formula for Simple interest is: Total Amount = Principal + Principal * Interest * Time

For Chase, FV = 2500 * (1 + 5%)⁴ = 2500 * 1.2155 = $3,038.77

For Citi, Total Amount = 2,500 + (2,500 * 6% * 4) = 2500 + 600 = $3,100

Therefore, you should prefer Citi, where you will have greater final amount accumulated