1. TLW find compound interest and depreciation.
8.3
TLW find compound interest and depreciation.

2. Compound Interest
You earn interest on capital AND previously earned interest.
Interest on interest

3. Simple Interest A gradual increase Initial value used to find interest
Unfair to the investor since there is actually more value than the capital
Total Value = 𝐶 1+ 𝑟 𝑛 𝑛
Total Interest = 𝐶 1+ 𝑟 𝑛 𝑛 −𝐶
Why?

4. Example
Lars invests Swedish krona (SEK) at a rate of 5.1% compounding yearly. Calculate the amount in Lars’s account after 4 years and find how much of that amount is interest, Give answers correct to 2 d.p.

5. Another Example
Giovanni’s bank manager told him that if he invests 3000 EUR now, compounding yearly, it will be worth 4600 EUR in 5 years’ time.

6. Another, another example
Marina is saving to buy a small boat that costs USD. She has USD in an account that pays 5.34% interest compounding yearly. How must Marina wait before she can buy the boat?
Setup:
Let’s use Solver to find the answer.

7. Compound Interest and the GDC
In APPS you will find Finance
Use TVM Solver
N = # of time periods ( # of years)
I = interest rate
Can be negative if we are computing depreciation
PV = principal (C)
This is relative to the investor. Money invested is outgoing and therefore entered with a negative sign.
If the money is borrowed, then it is positive.
PMT = extra payments (none)
Negative if money is borrowed
FV = final value
This is positive because it is paid to the investor at the end of investment
P/Y = payments per year, leave as 1
C/Y = compounding events per year
PMT END BEGIN = when to apply interest in the period
Place the cursor on what you’re solving for and press ALPHA ENTER to solve.

8. Again but with GDC
Marina is saving to buy a small boat that costs USD. She has USD in an account that pays 5.34% interest compounding yearly. How must Marina wait before she can buy the boat?

9. Subdivided Time Periods
Formula: 𝑇=𝐶 1+ 𝑟 100𝑘 𝑘𝑛
k = how many times compounded in one year
𝐼=𝐶 1+ 𝑟 100𝑘 𝑘𝑛 −𝐶 finds just the interest
Possible “k” in a year
Quarterly – 4 times
Weekly – 52
Daily – 365
Monthly – 12
Half yearly – 2
Actual Interest: Divide interest rate (nominal rate) by the number of times compounded in a year.

10. The bank in Grabiton is advertising a nominal yearly rate of 5% with compounding applied quarterly. State the number of compounding periods for a 3-year investment and find the actual interest rate applied after each time period.
Fleur invests 500 GBP in this bank for three years. Calculate the total capital in her account after this time.
Suppose Fleur invests this money at a rate of 5% p.a. compounding only once a year. How much less interest would she receive?

11. A Real-life Example
A bank in Australia is offering a “term-deposit” account with a choice of interest rates. As long as you leave your money with them for 2 years, you can get a nominal rate of
5.05% compounded monthly OR
5.10% compounded quarterly OR 5.15% compounded half-yearly OR
An actual yearly rate of 5.2%
Abigail has 7000 AUD to invest. Which is her best option?
Remember you must show your method on Papers 1 and 2 or lose all the marks.

12. Annoushka has 2736. 74 EUR in her bank account
Annoushka has EUR in her bank account. She has left her money there for exactly 3 years at a nominal rate of 4.1% p.a. compounding daily. Calculate, correct to the nearest EUR, how much Annoushka put in the account when she opened it. (Assume there were no leap years in that time.)
Check with GDC.

13. How does this connect to geometric sequence?
Simple interest– we add equal amounts
Compounded interest– we multiply equal amounts
This makes it a geometric sequence

14. A geometric sequence has third term 212.24 and fifth term 220.82.
If these are capital amounts in a an account offering r% interest at time periods, after 3 and 5 time periods, then find r and the initial amount, C, in the account to the nearest whole number.

15. Amanda has paid school fees for her son for seven years
Amanda has paid school fees for her son for seven years. In the first year, the fees were $ They have increased by 5% p.a. every year. Find how much Amanda has paid in total.
Sum a geometric sequence: 𝑆 𝑛 = 𝑢 1 𝑟 𝑛 −1 𝑟−1

16. Joe is saving for retirement
Joe is saving for retirement. He pays GBP into a bank account at the start of each year for n years. The account pays 7.1% interest compounding annually. Show that, after n years, the amount, A, that Joe has in the account is
𝐴= 𝑛 − 𝐺𝐵𝑃
If n is 12, calculate A.

17. Depreciation
Loss of value
Rate r is negative

18. Vijay has paid 300 000 Indian rupees (INR) for a car
Vijay has paid Indian rupees (INR) for a car. The car depreciates at a rate of 9% p.a. Calculate the value, V, of the car in 4 years’ time, giving your answer correct to the nearest INR.
Find the percentage loss over the 4-year period.
Find the new value.
Percentage loss = 𝑜𝑙𝑑−𝑛𝑒𝑤 𝑜𝑙𝑑 𝑥100%

19. Anthony bought a house for 380 000 USD 7 years ago
Anthony bought a house for USD 7 years ago. Since then, in his area, houses have increased in value by an average of 10 % p.a. for the first 5 years but then lost value at a rate of 4% p.a. for the last 2 years.
What is the value, V, of the house now? Give the answer to the nearest 1000 USD.