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Semenov [28]
2 years ago
15

Rebecca was advised to invest her £12000 life savings in a special High

Mathematics
2 answers:
madam [21]2 years ago
5 0

Answer:

(a)  Year 1: £12,540

     Year 2: £13,167

     Year 3: £13,964.85

     Year 4: £14,544.23

(b)  £2,544.23

(c)  21.2% (1 d.p.)

Step-by-step explanation:

<u>Simple interest formula</u>

A = P(1 + rt)

where:

  • A = final amount
  • P = principal
  • r = interest rate (in decimal form)
  • t = time (in years)

Given:

  • Principal = £12,000
  • Interest rates for each progressive year = 4.5%, 5%, 5.3% and 4.9%

<h3><u>Part (a)</u></h3>

<u />

<u>Year 1</u>

⇒ A = 12000(1 + 0.045)

⇒ A = £12,540

<u>Year 2</u>

⇒ A = 12540(1 + 0.05)

⇒ A = £13,167

<u>Year 3</u>

⇒ A = 13167(1 + 0.053)

⇒ A = 13964.851

⇒ A = £13,964.85

<u>Year 4</u>

⇒ A = 13964.851(1 + 0.049)

⇒ A = 14544.2287

⇒ A = £14,544.23

<h3><u>Part (b)</u></h3>

\begin{aligned}\sf Total \: interest & = \sf final \: amount - principal \: amount\\& = \sf 14544.23 - 12000\\& = \sf \£2,544.23\end{aligned}

<h3><u>Part (c)</u></h3>

<u />

\begin{aligned}\sf Percent & =\sf \left(\dfrac{Value}{Total\:value}\right) \times 100\\\\ \implies \textsf{Percent} & =\sf \dfrac{2544.23}{12000} \times 100\\\\ & = \sf 21.2\%\:\:(1\:d.p.) \end{aligned}

Evgesh-ka [11]2 years ago
3 0

#a

#1st year

\\ \rm\Rrightarrow 12000+0.045(12000)=12540

#2nd year

\\ \rm\Rrightarrow 12540+0.05(12540)=13167

#3rd year

\\ \rm\Rrightarrow 13167+0.053(13167)=13864.85

#4th year

\\ \rm\Rrightarrow 13864.85+13864.85(0.049)=14544.2

#b

Total interest

\\ \rm\Rrightarrow 14544.2-12000=£ 2544.2

#c

Percentage

\\ \rm\Rrightarrow \dfrac{2544.2}{12000}\times 100

\\ \rm\Rrightarrow 21.2\%

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======================================================

Explanation:

Let's say there are 100 households (just for the sake of simplicity). We are told that 90% of them have answering machines. So that means 90 households have answering machines. In addition, 50 households have answering machines and call waiting. Those 50 households are part of the 90 mentioned previously.

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----------------

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