The management of a golfing club purchased new lawn mowers for \$23\,000.
Using the flat rate depreciation method, with a rate of 12\% p.a., write a recursive rule for the value of the mowers after n years, V_{n+1} in terms of V_n and initial balance V_0.
Using the flat rate depreciation method, determine the value of the lawn mowers after four years.
Using the reducing balance depreciation method, with a rate of 16\% p.a., write a recursive rule for the value of the mowers after n years, B_{n+1} in terms of B_n and initial balance B_0.
Using the reducing balance depreciation method, calculate the value of the lawn mowers after four years.
After four years, which method results in the greater depreciation?
A particular piece of equipment, which has an initial value of \$8360, depreciates using the unit cost method by 22 cents per hour of use. On average, the equipment is used for 3800 hours per year.
Calculate the value of the equipment after three years.
If the equipment depreciated using flat rate depreciation of 10\% p.a. instead, calculate the value of the equipment after three years.
After how many years will the equipment be written off with a depreciated value of \$0 using the flat rate depreciation method?
Suppose that the reducing balance method is used instead, at a rate of 14\% p.a.. What will be the depreciated value of the equipment after 10 years?
Which of the three methods results in the lowest amount of depreciation?
The Andersons were offered a \$24\,800 loan to pay for a new car. Their loan is to be repaid in equal monthly payments of \$750 (except for the last month, when a smaller payment will be required to finish the repayment).
An interest of 10.8\% p.a. is calculated monthly on the reducing balance, before the monthly payments are made.
Write a recursive rule for the monthly balance of the loan, B_{n+1} in terms of B_n and initial balance B_0.
Calculate the least number of months needed to repay this loan plus interest.
Calculate the amount of the final repayment.
When the Andersons took out their loan, they had the choice of making monthly repayments of \$750 or quarterly repayments of \$2250. In either case, the loan would earn interest at a rate of 10.8\% p.a., calculated monthly on the reducing balance.
Was making monthly repayments of \$750 the best choice? Explain your answer.
Bart took out a loan to get his large pine trees removed, after they were affected by a massive storm. The loan of \$28\,000 was due to run for 8 years, earning interest at a rate of 6.5\% p.a., added monthly to the outstanding balance. Repayments of \$374.81 were made each month.
Write a recursive rule for the monthly balance of the loan, B_{n+1} in terms of B_n and initial balance B_0.
After 3 years, the rate changed to 7.5\% p.a. debited monthly. The repayment value didn't change. Find the outstanding balance at the time that the rate changed.
Find the actual term of the loan, to the nearest month.
Poppy is repaying a \$55\,000 house loan with interest calculated quarterly at a rate of 7\% p.a.. Quarterly repayments of \$1487.93 are being made to pay off the loan, and twenty such repayments have already been made.
Write a recursive rule for the quarterly balance of the loan, B_{n+1} in terms of B_n and initial balance B_0.
How much does Poppy have left to pay back on her loan after twenty payments?
How many quarters remain until the loan is paid off? Round your answer to the nearest whole number of quarters.
Poppy decides to change her repayments to \$250 per fortnight. The bank responds by adjusting the interest to be calculated fortnightly.
Calculate how many fortnights remain until the loan is paid off under this new system. Assume that there are 52 weeks in a year.
Will Poppy repay her loan more quickly by changing to the fortnightly repayment system?
Tricia inherited \$140\,000 from her aunt. She decides to invest this money into an account that pays 6.24\% p.a. in interest, compounded monthly.
If Tricia deposits her money into a perpetuity, what monthly payment will she receive?
If Tricia deposits her money into an annuity and withdraws \$1000 per month, how much will be left in the account after 1 year?
If Tricia deposits her money into an annuity and withdraws \$1500 per month instead, how long will it take for the value of her investment to drop below \$100\,000?
If Tricia deposits her money into an annuity and withdraws \$5000 per month instead, how long will her investment last for?
James is joining his friends on a holiday. To pay for the holiday and related expenses, he borrows \$10\,000. Interest is charged on this loan at a rate of 12.9\% per annum, compounded monthly.
For the first year of the loan, James makes interest-only repayments. Find the value of each repayment.
Over the next three years of the loan James makes equal monthly repayments, such that at the end of the 3 years his remaining balanced owed is \$3776.15. Find the size of his monthly repayment, to the nearest dollar.
James is to fully repay the outstanding balance of \$3776.15 after one final year. The first 11 monthly repayments will each be \$330. What will the value of the twelfth and final repayment be, so that the loan is fully repaid?
When a family bought their home they borrowed \$100\,000, earning interest at a rate of 9.4\% p.a., compounded quarterly. The loan is to be repaid over 26 years in equal quarterly repayments. Each repayment is made after the interest is compounded each quarter.
How much of the first quarterly repayment will go towards paying off the principal?
After 10 years the family inherit a large amount of money and decide to terminate the loan early, paying the remaining amount owed in a lump sum. Calculate the value of this lump sum.
Ursula has \$80\,000 to invest, and chooses an annuity that pays 6.4\% p.a. in interest, compounded monthly. She expects the investment to be fully exhausted after 15 years.
Find the size of the monthly withdrawals that Ursula can make. Round your answer to the nearest dollar.
Find the amount that Ursula has left in the investment after 2 years.
After two years, the interest rate of Ursula's investment was reduced to 6.2\% p.a. compounded monthly. If she continues to withdraw the same amount each month, for how many more months will her investment last? Round your answer to the nearest month.
If Ursula still wants her investment to last the full 15 years in total, what is the new monthly withdrawal that she should make after the interest rate is lowered?
Marge has won \$750\,000 in a lottery. She decides to place the money in an investment account that pays 4.5\% p.a. in interest, compounded monthly.
How much will Marge have in the investment account after 10 years? Round your answer to the nearest dollar.
After the 10 years, Marge decides to use her money to invest in an annuity, which pays 3.5\% p.a., compounded monthly.
If Marge withdraws \$6000 per month for her living expenses, how long will the annuity last? Each withdrawal is made after the interest is compounded each month.
Marge's accountant suggests that rather than purchase an annuity she places the money into a perpetuity instead, so that she will be able to leave some money to her grandchildren. If the perpetuity pays 3.5\% p.a., compounded monthly, find the monthly payment that Marge will receive.
Tom sells his mechanics business for \$340\,000 and invests this amount into a perpetuity. The account earns interest at a rate of 5.3\% p.a., calculated monthly.
What monthly payment will he receive from this investment?
Later, Tom converts his perpetuity into an annuity investment, earning interest at a rate of 3.7\% p.a. compounded monthly. For three years he makes further deposits of \$500 each month, immediately after interest is calculated. Find the value of the annuity after the three years.
After the three years, Tom increases his monthly payment. This new payment results in a balance of \$500\,000 after a further 2 years. Calculate the amount of his new monthly payment.
After retiring from work, Kerry received a superannuation payment of \$750\,000. She has two options for investing her money:
Option 1: Invest in a perpetuity that will provide fortnightly payments of \$887.04 for the rest of her life.
Option 2: Invest in an annuity that earns interest at a rate of 4.32\% p.a., compounded monthly.
Determine the annual interest rate for the perpetuity (Option 1). Assume that there are 52 weeks in a year. Give your answer as a percentage, rounded to two decimal places.
If Kerry chose the annuity (Option 2), then her balance at the end of the first year would be \$480\,242.00. Determine the monthly payment she would receive with this option.
Rosey is 54 and plans to retire at 65. To do this, she estimates that she needs \$600\,000. Her current superannuation fund has a balance of \$115\,000, and is delivering interest at a rate of 9.5\% p.a. compounded monthly.
Find the monthly contributions needed for Rosey to meet her retirement lump sum target.
In the final five years before retirement, Rosey doubles the monthly contribution found in part (a). Determine the new lump sum amount that she will have by her retirement age.
How much extra could Rosey expect if in the final 5 years, the interest rate was also increased, to a value of 11\% p.a. compounded monthly? Round your answer to the nearest \$1000.
A couple puts a \$50\,000 down-payment on a new home, and arranges to pay off the rest in monthly payments of \$1384 for 30 years at an interest rate of 8.5\% p.a., compounded monthly.
What was the selling price of the house?
How much interest will they have paid over the course of the loan?
After 6 years of repayments, how much is still owed?
After 6 years, the interest rate is increased by 0.9\%, and the couple must extend the period of the loan in order to pay it back in full. How much will they still owe after the original 30-year period?
If the couple still want to have the loan be fully repaid in the 30 years, determine the size of the monthly repayment they would need to repay after the interest rate change.