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6.05 Analysing investments with periodic payments

Interactive practice questions

To start saving money for retirement, Valentina invests $\$150$$150 each month at an interest rate of $6%$6%p.a., compounded monthly. Determine the future value in this annuity after $15$15 years. Round your answer to the nearest cent.

Easy
1min

Uther invests $\$2300$$2300 each year for $30$30 years into an account with an interest rate of $2.5%$2.5%p.a., compounded annually. Determine the future value $A$A of this annuity at the end of the investment period, rounding your answer to the nearest cent.

Easy
1min

Xavier invests $\$300$$300 each quarter for $30$30 years into an account with an interest rate of $8%$8%p.a., compounded quarterly. Determine the future value $A$A of this annuity at the end of the investment period, rounding your answer to the nearest cent.

Easy
1min

Using technology or otherwise, determine the minimum regular payment needed for semiannual payments with an interest rate of $3.5%$3.5%p.a., compounded semiannually for $20$20 years, to accumulate $\$15000$$15000.

Make sure you round your answer up to the nearest cent to make sure that enough is invested each period.

Easy
1min
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Outcomes

4.1.3.1

use a recurrence relation A_(n+1)=𝑟A_𝑛+𝑑 to model an annuity and investigate (numerically or graphically) the effect of the amount invested, the interest rate, and the payment amount on the duration of the annuity

4.1.3.2

solve problems involving annuities, including perpetuities as a special case, e.g. determining the amount to be invested in an annuity to provide a regular monthly income of a certain amount

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