Juliana plans to invest money for 10 years in an account paying 3.5% interest, compounded annually. She expects the annual inflation rate to be 2% per year throughout the 10-year period. Juliana would like her investment to be worth a real value of $ € 4000$, compared to current values, at the end of the 10-year period. She is considering two options.

METHOD 1 - (with $FV=4000$)

EITHER

$N=10$ $\\I=1.5$ $\\FV=4000$ $\\P/Y=1$ $\\C/Y=1$ A1 M1

Note: Award A1 for $(3.5-2=) 1.5$ seen and M1 for all other entries correct.

OR

$4000=A(1+0.015)^{10}$ A1 M1

Note: Award A1 for 1.5 or 0.015 seen, M1 for attempt to substitute into compound interest formula and equating to 4000.

THEN

$PV=3447$ A1

Note: Award A0 if not rounded to a whole number or a negative sign given.

METHOD 2 - (With FV including inflation)

calculate FV with inflation $4000 \times 1.02^{10}$ A1

$(=4875.977...)$

EITHER

$4000 \times 1.02^{10}=PV \times 1.035^{10}$ M1

OR

$N=10$ $\\I=3.5$ $\\FV=4875.977..$ $\\P/Y=1$ $\\C/Y=1$ M1

Note: Award M1 for their FV and all other entries correct.

THEN

$PV=3457$ A1

Note: Award A0 if not rounded to a whole number or a negative sign given.

METHOD 3 - (Using formula to calculate real rate of return)

real rate of return $=$ $1.47058...(\%)$ A1

EITHER

$4000=PV \times 1.0147058...^{10}$ M1

OR

$N=10$ $\\I=1.47058...$ $\\FV=4000$ $\\P/Y=1$ $\\C/Y=1$ M1

Note: Award M1 for all entries correct.

THEN

$PV = 3457$ A1

METHOD 1 - (Finding the future value of the investment using PV from part (a))

$N=10$ $\\I=3.5$ $\\PV=3446.66...$ from Method (1) OR $3456.67...$(from Methods 2, 3) $\\P/Y=1$ $\\C/Y=1$ M1

Note: Award M1 for interest rate 3.5 and answer to part (a) as PV.

$FV=4861.87$ OR $4875.97$ A1

so payment required (from TVM) will be \294$OR$$295$ A1

Note: Award A0 if a negative sign given, unless already penalized in part (a).

METHOD 2 - (Using FV)

$N=10$ $\\I=3.5$ $\\PV=-1000$ $\\FV=4875.977...$ $\\P/Y=1$ $\\C/Y=1$ A1 M1

Note: Award A1 for $I=3.5$ and $FV= \pm 4875.977...$, M1 for all other entries correct and opposite PV and FV signs.

$PMT = 295(295.393)$ A1

Note: Correct 3sf answer is 295, however accept an answer of 296 given that the context supports rounding up. Award A0 if a negative sign given, unless already penalized in part (a).