Interactive practice questions
Victoria invests $\$400000$$400000 in an annuity paying $3.2%$3.2% interest per annum. The annuity is designed to give her an annual payment of $\$47372$$47372 for $10$10 years. The amortisation table for this annuity is shown below in dollars. Some of the information is missing.
| Payment number ($n$n) | Payment made | Interest earned | Reduction in principal | Balance of annuity |
|---|---|---|---|---|
| $0$0 | $0$0 | $0$0 | $0$0 | $400000$400000 |
| $1$1 | $47372.00$47372.00 | $12800.00$12800.00 | $34572.00$34572.00 | $-$− |
| $2$2 | $47372.00$47372.00 | $11693.70$11693.70 | $35678.30$35678.30 | $329749.70$329749.70 |
| $3$3 | $47372.00$47372.00 | $10551.99$10551.99 | $36820.01$36820.01 | $292929.69$292929.69 |
| $4$4 | $47372.00$47372.00 | $9373.75$9373.75 | $37998.25$37998.25 | $254931.44$254931.44 |
| $5$5 | $47372.00$47372.00 | $8157.81$8157.81 | $-$− | $215717.25$215717.25 |
| $6$6 | $47372.00$47372.00 | $6902.95$6902.95 | $40469.05$40469.05 | $175248.20$175248.20 |
| $7$7 | $47372.00$47372.00 | $5607.94$5607.94 | $41764.06$41764.06 | $133484.14$133484.14 |
| $8$8 | $47372.00$47372.00 | $-$− | $-$− | $90383.63$90383.63 |
| $9$9 | $47372.00$47372.00 | $2892.28$2892.28 | $44479.72$44479.72 | $45903.91$45903.91 |
| $10$10 | $47372.00$47372.00 | $1468.93$1468.93 | $45903.07$45903.07 | $0.84$0.84 |
The balance of the annuity after one payment has been made is:
$\$365428.00$$365428.00
$\$387200.00$$387200.00
$\$400000$$400000
$\$352628.00$$352628.00
The reduction in the principal of the annuity after payment number $5$5 is:
$\$28624.50$$28624.50
$\$44419.44$$44419.44
$\$47372.00$$47372.00
$\$39214.19$$39214.19
The amount of interest earned in the $8$8th year is:
$\$4250.11$$4250.11
$\$38829.02$$38829.02
$\$43100.51$$43100.51
$\$4271.49$$4271.49
Iain invests $\$190000$$190000 at a rate of $7%$7% per annum compounded annually. At the end of each year he withdraws $\$14300$$14300 from the investment after the interest is paid and the balance is reinvested in the account.
We will use the financial solver on our CAS calculator to determine how long the annuity lasts.
Carl invests $\$190000$$190000 at a rate of $12%$12% per annum compounded monthly. At the end of each month he withdraws $\$3900$$3900 from the investment after the interest is paid and the balance is reinvested in the account.
We will use the financial solver on our CAS calculator to determine how long the annuity lasts.