Loans, Investments, and Annuities

Question 1

Use the compound interest formula to determine:
The future amount of a $5000 investment at 3.2% per annum, compounding quarterly for 5 years.

Answer 1

Question 2

Use the compound interest formula to determine:
The principal required to reach $25,000 at 4.7% per annum, compounding monthly for 8 years.

Answer 2

Question 3

Use the compound interest formula to determine:
The interest rate required to grow $4000 to $4200 over 3 years, when compounding every 6 months

Answer 3

Question 4

Jeffrey borrows $3500 at a rate of 6.5% p.a. (compounding monthly) which is to be paid back with monthly instalments of $711.42.
Write a recurrence relation to describe this situation.

Answer 4

Question 5

Craig is starting a new annuity account and will invest $500 every six months for 10 years at 6% p.a. compounded six-monthly.
a. Calculate the future value of the annuity. (Hint: don’t use recurrence).
b. How much of this value is interest that had been earned?

Answer 5

Question 6

Genevieve’s grandparents set up a perpetuity to help pay for her tertiary education. They invest $125,000 at an interest rate of 4.5% p.a., with the interest rate for this perpetuity compounded quarterly.
a. Calculate the amount Genevieve can pay off her university fees each quarter.

Answer 6

Question 7

A local community group, Rotex, raises money to set up a fund to give a scholarship to a disadvantaged young person in the community. The group invests in a perpetuity that is guaranteed an interest rate of 7.5% p.a. Determine the amount to be invested in this perpetuity to provide a regular monthly income of $700.

Answer 7

Question 8

Calculate the second month’s interest on a $70 000 reducing balance loan at 5.5% p.a. if the monthly repayment is $750.

Answer 8

Question 9

Calculate the length of time required for $2650 to grow to $3500 at 8.4% p.a. compounded monthly. Give your answer to the nearest month.

Answer 9

Question 10

Which annuity is depost and which is withdrawal

Answer 10

Left is deposit right is withdrawal

Question 11

When the compounding period is missing from a compound interest question, what method do you use to find it?

Answer 11

Divide the final amount by the principle, should look like
(1.0007)N = 1.32067

Then, trial and error to find it out. If you use a number lower or higher for N, the equation will be incorrect and will not equal 1.32067 e.g.

Question 11

When the interest rate is missing from a compound interest question, what method do you use to find it?

Answer 11

Divide the final amount by the principle, should look like
(1+i)6 = 1.05

Then, square root the value by the compounding period, and subtract 1 after to have the interest rate looking like 0.008164

If it trying to find per annum, multiply by 2, 4, 12, etc. if it is bi-annually, quarterly, or monthly, etc.

Question 12

When the principle is missing from a compound interest question, what method do you use to find it?

Answer 12

Divide the final amount by the other side of the equation entirely, brackets and compounding period included.