5.04 Other variations in compounding

Gwen has \$2000 cash set aside for a holiday in 2022. Her bank account offers 2\% interest per annum, compounded annually.

Marge has \$3000 in a savings account which earns 2\% interest per annum, compounded annually.

Mario has an arrangement with his work where \$11\,274 from his salary will go towards an investment at the start of a year of his choosing. The investment will be withdrawn in 2031 when he retires, and offers 3.75\% interest per annum, compounded annually.

Peter has \$4947 to place in an investment account which will earn 1.25\% interest per annum, compounded annually.

Consider the following two investment options for a principal of \$14\,000:

• Option 1: Earns 2\% per annum over 12 years, compounded annually.

• Option 2: Earns 3.5\% per annum over 9 years, compounded annually.

Consider the following two investment options for a principal of \$13\,000:

• Option 1: Earns 3\% per annum over 10 years, compounded monthly.

• Option 2: Earns 3.5\% per annum over 7 years, compounded monthly.

Sharon is considering whether it would be more beneficial for her to invest her money now or 7 years down the track. For an initial investment of \$5000, the function \\FV = 5000(1.027)^n models the value her money will grow to in n years.

Deborah would like to invest \$80\,000 and is considering two investment options:

• Investment option A returns 3.4\% interest per annum, compounded quarterly over 12 years.

• Investment option B returns 2.7\% interest per annum, compounded quarterly over 14 years.

Find how many years it will take a \$370 investment, compounded annually at 6.6\%, to:

Serge needs to save \$2400 for a camping trip in the mountains. How many years will it take him to reach his savings goal of \$2400 if he invests \$1800 in a savings account that accrues interest at:

Isabelle is considering whether it would be greatly beneficial for her to invest her money now rather than 5 years down the track. For an initial investment of \$3000, the function \\ A = 3000 \left(1.026\right)^{t} models how value her money will grow to in t years.

Regardless of whether she invests now or in 5 years time, she will close the account when she retires (more than 8 years in the future).

How many times more will her closing balance be if she starts investing now rather than 5 years down the track? Give your answer correct to two decimal places.

Find the principal, P, that would need to be invested at 10\% p.a. compounded quarterly to accumulate \$6500 in 10 years. Give your answer to the nearest dollar.

Find the amount, P, that would need to be invested at 6\% p.a. compounded monthly to accumulate \$5600 in 9 years. Give your answer to the nearest dollar.

Find the amount, P, that Charlie would have to deposit into a special interest bearing account that pays interest of 5\% p.a. compounded semiannually so that after 9 years he would have \$9800.

Find the principal, P, that would need to be invested at 6\% p.a. compounded semiannually to accumulate \$7600 in 9 years. Give your answer to the nearest dollar.

Find the amount, P, that Mario would have to deposit into a special interest bearing account that pays interest of 6\% p.a. compounded quarterly so that after 5 years he would have \$7180.

After 8 years, Ally's investment is worth \$24\,900. Her investment grew at a rate of 12\% p.a. compounded monthly. How much money did Ally initially invest?

After 11 years, Kyle paid back his loan which had acuumulated to \$36\,840. His loan had an interest rate of 12\% p.a. compounded quarterly. How much money did Kyle initially borrow?

Mae's investment into a 20-year 2.33\% p.a. corporate bond grew to \$13\,600. Calculate the size of Mae's initial investment if interest was compounded:

Carl is expecting a Christmas bonus of \$1800 in 4 months time. What is the most he can borrow now, at a rate of 4.1\% p.a. compounded daily, and still be able to pay off the loan with his bonus?

Scott wants to have \$1500 at the end of 5 years. If the bank offers 2.3\% p.a. compounded annually, how much should he invest now?

Tom wants to put a deposit on a house in 4 years time. In order to finance the \$12\,000 deposit, he decides to put some money into a high interest savings account that pays \\ 5\% p.a. interest, compounded monthly. If P is the amount of money that he must put into his account now to accumulate enough for the deposit, find P.

Ursula has just won \$30\,000. She decides to invest some of her winnings into a retirement fund which earns 8\% interest p.a., compounded yearly. When she retires in 29 years, she wants to have \$52\,000 in her fund.

How much of her winnings should Ursula invest now to achieve this?

Victoria has been promised an inheritance of \$70\,000 in 5 years time. What is the most she can borrow now at a rate of 7\% p.a. compounded annually, and still be able to pay off the loan with her inheritance?

Rochelle is planning to make an investment which accumulates monthly compound interest at a rate of 4.8\% p.a. If she aims to have her investment reach \$90\,000 after 11 years, find the principal amount that she should invest.

The sales of a company grow from \$450 to \$730 over 8 years. What is the percentage growth per annum, r? Give your answer as a percentage to two decimal places, and assume growth compounds annually.

What annual interest rate, r, is required to return \$670 from \$300 over 10 years? Give your answer as a percentage to two decimal places and assume growth compounds quarterly.

At what annual compound interest rate, r, must Joanne invest \$220 if she wishes to triple her money in 17 years? Give your answer as a percentage correct to two decimal places.

Bart is planning to invest \$110\,000 into a saving scheme which accumulates interest weekly. If he aims to have his investment reach \$120\,000 after 2 years, what interest rate per annum, r, will he need? Round your answer to four decimal places.

\$3940 is invested at a simple interest rate of 4\% for 14 years. At what annual compound interest rate, r, must the principal be invested to grow to the same amount in the same amount of time? Give your answer as a percentage correct to two decimal places.

At what annual compound interest rate, r, must you invest your money so that \$1000 grows twofold in 16 years? Give your answer as a percentage, correct to two decimal places.

Han opened a savings account at the beginning of February 2011, where the interest is compounded monthly. His statements for March, April and May show his account balance at the beginning of each month:

If n is the least number of whole years it will take to return \$464 from \$400, invested at 4\% compounding semi-annually, find n.

What is the least number of years, n, that it will take to return \$336 from \$310, invested at 1.6\% compounding annually?