Ch.5 Flashcards
Suppose you invest $1000 for one year at 5% per year. What is the future value in one year?
Future Value (FV) = $1000 × (1 + 0.05) = $1050
What is the formula for simple interest
FV=PV+PV x r x t
Diff between simple interest and compound interest
Simple interest - earn interest on principal only
Compound interest - earn interest on principal and reinvested interest
Suppose you had a relative deposit $10 at 5.5% interest 200 years ago.
FV = $10 × (1.055)200 = $447,189.84
Suppose your company expects to increase unit sales of widgets by 15% per year for the next 5 years.
If you currently sell 3 million widgets in one year, how many widgets do you expect to sell in 5 years?
FV = 3,000,000 × (1.15)5 = 6,034,072 units
Suppose you have $500 to invest and you believe that you can earn 8% per year over the next 15 years.
- How much would you have at the end of 15 years using compound interest?
- How much would you have using simple interest?
How much would you have at the end of 15 years using compound interest? = 1586
How much would you have using simple interest?
1100
Suppose you need $10,000 in one year for the down payment on a new car.
If you can earn 7% annually, how much do you need to invest today?
𝑃𝑉=$9,345.79
Your parents set up a trust fund for you 10 years ago that is now worth $19,671.51.
If the fund earned 7% per year, how much did your parents invest?
𝑃𝑉= $19,671.51/〖(1+0.07)〗^10 =$10,000
the longer the time period, the _______ the present value.
lower
For a given time period - the higher the interest rate, the ______ the present value.
smaller
You are looking at an investment that will pay $1200 in 5 years if you invest $1000 today.
What is the implied rate of interest?
r = (1,200/1,000)1/5 – 1 = 0.03714 or 3.714%
Suppose you are offered an investment that will allow you to double your money in 6 years.
You have $10,000 to invest. What is the implied rate of interest?
r = (20,000/10,000)1/6 – 1 = 0.122462 or 12.25%
Suppose you have a 1-year-old son and you want to provide $75,000 in 17 years towards his college education. You currently have $5000 to invest.
What interest rate must you earn to have the $75,000 when you need it?
r = (75,000/5,000)1/17 – 1 = 0.172688 or 17.27%
Suppose you are offered the following investment choices:
- You can invest $500 today and receive $600 in 5 years. The investment is considered low risk.
- You can invest the $500 in a bank account paying 4%.
What is the implied interest rate for the first choice and which investment should you choose?
- r = (600 / 500)1/5 – 1 = 3.714%
? In this case, you would choose to repay $600 because you would be paying a lower rate.
You want to purchase a new car and you are willing to pay $20,000.
If you can invest at 10% per year and you currently have $15,000, how long will it be before you have enough money to pay cash for the car?
t = ln(20,000/15,000)/ln(1+0.10) = 3.02 years
