Compound Interest Outcomes. Solve problems about compound interest. Solve problems about appreciation and depreciation.

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1 1 Compound Interest Outcomes Solve problems about compound interest. Solve problems about appreciation and depreciation.

2 2 Interest normally works as a single percentage increase. e.g is put in a savings account with a 2% interest rate per annum / per year. How much money is in the account after one year? Interest = = 100 Total savings = = 5100

3 3 When interest is applied multiple times, it is called compound interest. We can calculate interest year-on-year or use a formula: Formula: F = P 1 + i t F = final value the value of the investment after some amount of time. P = principal the initial investment. i = the interest rate as a decimal (e.g. 8% = 0.08). t = duration of investment.

4 4 e.g is put in a savings account with a 2% interest rate per annum / per year. i. How much money is in the account after two years? F = P 1 + i t F = F = F = 5202 F =? P = 5000 i = 2% = 0.02 t = 2 years

5 5 e.g is put in a savings account with a 2% interest rate per annum / per year. i. How much money is in the account after three years? F = P 1 + i t F = F = F = F =? P = 5000 i = 2% = 0.02 t = 3 years

6 6 In each of the following, find the final value and total interest of the investment: Principal Interest Rate Time Final Value Interest % % % % % 3

7 7 e.g. A company takes out a loan to buy equipment. The loan terms are 4% per annum for three years. The company pays back a total of What was the value of the initial loan? F = P 1 + i t = P = P = P P = P = F = P =? i = 4% = 0.04 t = 3 years

8 8 e.g was invested at i% per annum for two years. After two years, the investment was worth Find the interest rate. F = P 1 + i t = i = 1 + i = 1 + i = 1 + i 1.03 = 1 + i i = 0.03 = 3%

9 9 2014(S) OL P1 Q OL P1 Q1 a) A sum of is invested in an eight-year government bond with an annual equivalent rate (AER) of 6%. Find the value of the investment when it matures in eight years time. b) A different bond gives 20% interest after 8 years. Calculate the AER for this bond. What sum of money invested at 6% per annum compound interest will amount to in 7 years? Give your answer correct to the nearest euro.

10 OL P1 Q was invested for 2 years at compound interest. a) The rate of interest for the first year was 4%. Find the amount of the investment at the end of the first year. b) The amount of the investment at the end of the second year was Find the rate of interest for the second year.

11 11 Solve Problems about Ap/Depreciation The value of assets changes over time. When an asset s value increases, we say it appreciates. When an asset s value decreases, we say is depreciates. Any asset can appreciate or depreciate, but we would often see real estate, savings accounts/bonds, and certain goods like gold appreciate; while cars, and electronics will depreciate. The interest formula still works: F = P 1 + i t, however remember to use a negative interest rate for depreciation.

12 12 Solve Problems about Ap/Depreciation e.g. A house in Dublin cost in It appreciated in value by 3% each year. How much was it worth in 2007? e.g. In mid-january 2017, 1 bitcoin was worth $ bitcoin was valued at $ in mid-december. Calculate its average monthly appreciation correct to two decimal places. e.g. In response to the financial crisis of the late 00s, the government introduced National Solidarity Bonds. Currently, a 10 year savings bond nets 16% tax free at the end of 10 years. What is the annual earnings rate (AER) on a 10 year bond?

13 13 Solve Problems about Ap/Depreciation e.g. A car is bought for If it decreases in value by 1% per month, how much is it worth after one year? e.g. A 16GB iphone 6 cost $100 on amazon in January In January 2015, the same phone cost $649. What was the annual depreciation rate? e.g. In mid-january 2018, 1 bitcoin was worth $ As of mid-march, 1 bitcoin was worth $ What was the monthly depreciation rate on bitcoin over this period?

14 OL P1 Q OL P1 Q7 Solve Problems about Ap/Depreciation A new machine is bought for Its value depreciates by 15% each year for five years. Find the value of the machine at the end of the five years. Mary bought a new car for on the 1st July The value of the car depreciated at a compound rate of 15% each year. Find the value of the car, correct to the nearest euro, on the 1st July 2014.

LCOL. A different investment bond gives 15% interest after 6 years. Calculate the AER for this bond.

LCOL. A different investment bond gives 15% interest after 6 years. Calculate the AER for this bond. LCOL A sum of 3000 is invested in a five-year government bond with an annual equivalent rate (AER) of 3%. Find the value of the investment when it matures in five years time. A different investment bond