Annuities Topic Test
Annuities · MST-12-S2-03
Maths Standard Year 12 · All 3 lessons · MC checkpoint plus separate short-answer practice
L1, Annuities
L2, Future Value of Annuities
L3, Present Value of Annuities
25 MC
8 SA
~55 min
0/25
MC Checkpoint
Answer questions to see your score.
Recommended next step after MC checkpoint
Complete the 25 multiple choice questions to unlock a sharper next move. The short-answer section below is separate practice.
Part A, Multiple Choice (1 mark each, 25 marks total)
A a single lump sum invested once and left to compound
B an interest rate that changes from period to period
C a loan repaid in one payment at the end of the term
D a stream of equal payments made at regular intervals
D, a stream of equal payments made at regular intervals. Annuities use regular equal deposits or withdrawals.
A $3$
B $36$
C $12$
D $156$
B, $36$. $3 \times 12 = 36$.
A $0.005$
B $0.06$
C $0.5$
D $0.0005$
A, $0.005$. $0.06 \div 12 = 0.005$.
A the lump sum needed today to fund those payments
B the interest earned in the first period only
C what regular deposits grow to in the future
D the total of the payments before any interest
C, what regular deposits grow to in the future. Future value accumulates payments forward.
A the balance of the account at the end of the term
B the lump sum today equivalent to future regular payments
C the sum of all the payments with no discounting
D the interest rate per compounding period
B, the lump sum today equivalent to future regular payments. Present value discounts future payments back to today.
A $FV = M\dfrac{1-(1+r)^{-n}}{r}$
B $FV = M(1+r)^n$
C $FV = M\dfrac{r}{(1+r)^n-1}$
D $FV = M\dfrac{(1+r)^n-1}{r}$
D, $FV = M\dfrac{(1+r)^n-1}{r}$. This is the taught FV formula.
A $PV = M\dfrac{(1+r)^n-1}{r}$
B $PV = M(1+r)^{-n}$
C $PV = M\dfrac{1-(1+r)^{-n}}{r}$
D $PV = M\dfrac{r}{1-(1+r)^{-n}}$
C, $PV = M\dfrac{1-(1+r)^{-n}}{r}$. This is the taught PV formula.
A $24$
B $2$
C $12$
D $104$
A, $24$. $2 \times 12 = 24$.
A $100\dfrac{1-(1.01)^{-12}}{0.01}$
B $100(1.01)^{12}$
C $100\dfrac{(1.01)^{12}-1}{12}$
D $100\dfrac{(1.01)^{12}-1}{0.01}$
D, $100\dfrac{(1.01)^{12}-1}{0.01}$. Use the FV annuity formula.
A $5$
B $60$
C $12$
D $30$
B, $60$. Five years of monthly payments gives $60$.
A present value
B the future value of the repayments
C the regular repayment $M$
D the interest rate per period
A, present value. A loan amount today is the present value of future repayments.
A unchanged
B smaller
C larger
D zero
C, larger. Each payment earns interest for one extra period.
A $200$
B $210$
C $20$
D $2\,000$
D, $2\,000$. With no interest, total value is $200 \times 10$.
A $14\,400$
B $3\,600$
C $1\,200$
D $62\,400$
A, $14\,400$. There are 48 payments, so $300 \times 48 = 14\,400$.
A $(0.004)^{60}$
B $(1.004)^{60}$
C $(1.04)^{60}$
D $(1.004)^{250}$
B, $(1.004)^{60}$. Use $1+r = 1.004$ and exponent $60$.
A larger
B unchanged
C smaller
D equal to the total of the payments
C, smaller. Higher discount rates reduce present value.
A the required regular payment
B the number of payments needed
C the interest rate per period
D the present value of the account
A, the required regular payment. Solving for $M$ gives the regular deposit.
A $0.048$
B $0.4$
C $0.0004$
D $0.004$
D, $0.004$. $0.048 \div 12 = 0.004$.
A $5.08$
B $7\,867.20$
C $239.34$
D $786.72$
B, $7\,867.20$. $200 \times 39.336 = 7\,867.20$.
A $2\,586.25$
B $9.67$
C $25\,862.50$
D $551.73$
C, $25\,862.50$. $500 \times 51.725 = 25\,862.50$.
A The total amount deposited
B The final balance of the account
C The number of years in the term
D The payment period
D, The payment period. Rate, periods and payments must use matching units.
A $300$
B $25$
C $12$
D $1\,300$
A, $300$. $25 \times 12 = 300$.
A $576\,000$
B $48$
C $250$
D $11\,952$
C, $250$. $12\,000 \div 48 = 250$.
A inflation is subtracted from every payment
B future payments are discounted for interest
C the bank charges a fee on each payment
D the payments are made at the start of each period
B, future payments are discounted for interest. Money now can earn interest, so future payments are worth less today.
A Round the interest rate to one decimal place before starting
B Multiply the payment by the number of years
C Convert every amount to a percentage of the total
D Identify FV or PV, payment amount, rate per period and number of periods
D, Identify FV or PV, payment amount, rate per period and number of periods. Correct setup depends on these quantities.
Part B, Short Answer (separate practice)
(a) $n = 48$.
(b) It is a future value question.
(a) $FV = 200\dfrac{(1.005)^{36}-1}{0.005}$.
(b) $FV \approx \$7\,867$.
(a) $M \approx \$447.72$.
(b) Rounding to $448 helps make sure the target is reached.
(a) $PV = 600 \times 77.225 = \$46\,335$.
(b) It is the lump sum today equivalent to the payments.
(a) $PV = 500\dfrac{1-(1.004)^{-60}}{0.004}$.
(b) $PV \approx \$26\,625$.
(a) $M \approx \$1\,584.90$.
(b) Total $\approx \$380\,376$.
(a) Saving is FV; mortgage and pension withdrawals are PV.
(b) Savings grow forward; loans and pensions value future payments today.
(a) $r = 0.006$.
(b) $n = 72$.
Annuities Complete
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