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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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