investments and loans

Question 1

what is the formula for simple interest?

Answer 1

I = PRN

where I - interest
P - principal
R - rate
N - number of years

Question 2

what is the formula for the future value of compound interest?

Answer 2

FV = PV(1+r)^n

PV = FV
———
(1+r)^n

where FV - future value
PV - present value
r - rate
n - number of compounding time periods

Question 3

what is the formula for compound interest found or earned?

Answer 3

I = FV - PV

where I - interest (compounded) earned
FV - future value
PV - present value

Question 4

how is a simple interest graph formed?

Answer 4

1. construct a table of values for I and n using the simple interest formula
2. draw a number plane with n the horizontal axis and I the vertical axis. plot the points
3. join the points to make a straight line

Question 5

how is a compound interest graph formed?

Answer 5

1. construct a table of values for I and n using the compound interest formula
2. draw a number plane with n the horizontal axis and I the vertical axis. plot the points
3. join the points to make an exponential curve

Question 6

what is the formula for appreciation?

Answer 6

FV = PV(1+r)^n

where FV - future value
PV - present value
r - rate of appreciation
n - number of compounding time periods

Question 7

what is inflation?

Answer 7

inflation is the annual percentage change in the Consumer Price Index (CPI), calculated using the formula
FV = PV(1+r)^n

Question 8

what are shares?

Answer 8

shares are part ownership of a company, bought and sold on the stock market, with the intention of buying and then selling at a higher price, and bought and sold using a broker; the Goods and Service Tax (GST) of 10% is charged for buying and selling shares

Question 9

Lucy bought 500 shares at a market value of $6.80 each. brokerage fees incurred were $33 including GST. what is the total cost of purchasing the shares?

Answer 9

cost = (number of shares x price) + brokerage fee
= (500 x 6.8) + 33

= $3433
∴ cost of the shares is $3433.

Question 10

what is a dividend?

Answer 10

a dividend is a payment given as an amount per share or a percentage of the issued price

Question 11

how is dividend yield calculated?

Answer 11

dividend yield = (annual dividend
————————
market price)
x 100

Question 12

how is dividend calculated?

Answer 12

dividend = dividend yield x market price

Question 13

what is the dividend yield (to two decimal places) on a share with a market price of $33.70 and a dividend of $0.84 per share

Answer 13

dividend yield = (annual dividend
————————-
market price)
x 100

= 0.84
—— x 100
33.7

= 2.49258…
= 2.49% (2 decimal places)

Question 14

what is the total dividend received on 500 shares with a market price of $4.80 and a dividend yield of 5.2%?

Answer 14

dividend = dividend yield x market price

= 0.052 x 4.8
= 0.2496
0.2496 x 500
= $124.80

Question 15

what is the formula for declining-balance depreciation?

Answer 15

S = V0(1-r)^n

where S - salvage value or current value of an item
V0 - purchase price of the item
r - rate of depreciation
n - number of time periods

Question 16

Eva purchased a new car two years ago for $32000. during the first year it had depreciated by 25% and during the second it had depreciated 20% of its value after the first year. what is the current value of the car?

Answer 16

S = V0(1-r)^n
= 32000 x (1-0.25)^1
= $24000

= 24000 x (1-0.20)^1
= $19200

∴ current value is $19200

Question 17

how are loan repayments calculated?

Answer 17

total to be paid = loan payment x number of repayments

total to be paid = principal + interest

Question 18

how are credit card interest rates calculated?

Answer 18

daily interest rate =
annual interest rate
—————————-
365

FV = PV(1+r)^n
I = FV - PV

where FV - amount owing on the credit card
PV - principal is the purchases made on the credit card plus the outstanding balance
r - rate of interest per compounding time period expressed as a decimal
n - number of compounding time periods
I - interest (compound) charged on the outstanding balance

Question 19

Samantha has a credit card with a compound interest rate
of 18% p.a. and no interest-free period. Samantha used her credit card to pay for clothing costing $280. she paid the credit card account 14 days later. what is the total amount she paid for the clothing, including the interest charged?

Answer 19

FV = PV(1+r)^n

= 280 (1+0.18) ^14
——
365

= 281.93935…
= $281.94

Question 20

Hilary has a debit of $6000 on a credit card with an interest rate of 14.75% p.a. that compounds daily. she decided to transfer the balance to a new card with a 0% balance transfer for 6 months. however, after 6 months the new card reverted to an interest rate of 19.75% p.a that compounds daily. is Hilary better off after 12 months?

Answer 20

old card: FV = PV(1+r)^n
= $6000 (1+0.1475)^365
———
365
≈ $6953.39

new card: FV = PV(1+r)^n
= 6000(1+0.1975)^182.5
———
365
≈ 6622.57

savings: 6953.39 - 6622.57
= $330.82
∴ Hilary is better off with the new card by $330.82.