SPM.2.SL.TZ0.3

pestleMathematicsAASLPaper 2SPM· sl-1-4-financial-apps-compound-int-annual-depreciationsource ↗

On 1st January 2020, Laurie invests $P in an account that pays a nominal annual interest rate of 5.5 %, compounded quarterly.

The amount of money in Laurie’s account at the end of each year follows a geometric sequence with common ratio, r.

Find the value of r, giving your answer to four significant figures.

[3]

Laurie makes no further deposits to or withdrawals from the account.

Find the year in which the amount of money in Laurie’s account will become double the amount she invested.

[3]

Markscheme / solution

${\left( {1 + \frac{{5.5}}{{4 \times 100}}} \right)^4}$ (M1)(A1)

1.056 A1

[3 marks]

EITHER

$2P = P \times {\left( {1 + \frac{{5.5}}{{100 \times 4}}} \right)^{4n}}$ OR $2P = P \times {\left( {{\text{their}}\,\left( a \right)} \right)^m}$ (M1)(A1)

Note: Award (M1) for substitution into loan payment formula. Award (A1) for correct substitution.

PV = ±1
FV = $\mp$ 1
I% = 5.5
P/Y = 4
C/Y = 4
n = 50.756… (M1)(A1)

PV = ±1
FV = $\mp$ 2
I% = 100(their (a) − 1)
P/Y = 1
C/Y = 1 (M1)(A1)

THEN

⇒ 12.7 years

Laurie will have double the amount she invested during 2032 A1

[3 marks]

Examiners’ report

[N/A]