Solved: Sophia pays $200 into a bank account at the end of each month. The annual... [IB Mathematics Applications & Interpretation (Math AI)]

Sophia pays $200 into a bank account at the end of each month. The annual interest paid onmoney in the account is 3.1% which is compounded monthly.The average rate of inflation per year over the 5 years was 2%.

Question

SLPaper 1

Sophia pays $$ 200$ into a bank account at the end of each month. The annual interest paid onmoney in the account is $3.1 %$ which is compounded monthly.

The average rate of inflation per year over the $5$ years was $2 %$ .

Find the value of her investment after a period of $5$ years.

[3]

Verified

Solution

* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.

Number of time periods $12 \times 5 = 60$ (A1)

N = $60$
I% = $3.1$
PV = $0$
PMT = $200$
P/Y = $12$
C/Y = $12$
Value $($) 12, 961.91$ (M1)A1

[3 marks]

Find an approximation for the real interest rate for the money invested in theaccount.

[2]

Verified

Solution

METHOD 1

Real interest rate $= 3.1 - 2.0 = 1.1 %$ (M1)A1

METHOD 2

$\frac{1 + 0.031}{1 + 0.02} = 1.01078 \dots$ (M1)

$1.08 %$ (accept $1.1 %$ ) A1

[2 marks]

Hence find the real value of Sophia’s investment at the end of $5$ years.

[2]

Verified

Solution

N = $60$
I% = $1.1$
PV = $0$
PMT = $200$
P/Y = $12$
C/Y = $12$
$($) 12, 300 (12, 330.33 \dots)$ (M1)A1

Note: Award A1 for $$ 12, 300$ only.

[2 marks]

Question

SLPaper 1

Sophia pays $$ 200$ into a bank account at the end of each month. The annual interest paid onmoney in the account is $3.1 %$ which is compounded monthly.

The average rate of inflation per year over the $5$ years was $2 %$ .

Find the value of her investment after a period of $5$ years.

[3]

Verified

Solution

Number of time periods $12 \times 5 = 60$ (A1)

N = $60$
I% = $3.1$
PV = $0$
PMT = $200$
P/Y = $12$
C/Y = $12$
Value $($) 12, 961.91$ (M1)A1

[3 marks]

Find an approximation for the real interest rate for the money invested in theaccount.

[2]

Verified

Solution

METHOD 1

Real interest rate $= 3.1 - 2.0 = 1.1 %$ (M1)A1

METHOD 2

$\frac{1 + 0.031}{1 + 0.02} = 1.01078 \dots$ (M1)

$1.08 %$ (accept $1.1 %$ ) A1

[2 marks]

Hence find the real value of Sophia’s investment at the end of $5$ years.

[2]

Verified

Solution

N = $60$
I% = $1.1$
PV = $0$
PMT = $200$
P/Y = $12$
C/Y = $12$
$($) 12, 300 (12, 330.33 \dots)$ (M1)A1

Note: Award A1 for $$ 12, 300$ only.

[2 marks]

Sophia pays $200 into a bank account at the end of each month. The annual interest paid onmoney in the account is 3.1% which is compounded monthly.The average rate of inflation per year over the 5 years was 2%.

Related topics

Sophia pays $200 into a bank account at the end of each month. The annual interest paid onmoney in the account is 3.1% which is compounded monthly.The average rate of inflation per year over the 5 years was 2%.

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