Question

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

Interest Savings account, but she had to agree not to touch it for 4 years.
The interest rates for the 4 year period were 4.5%, 5%, 5.3% and 4.9% respectively.
(a) Calculate the value of her savings at the end of each year.
(b) What was the total interest that had accrued on her account?
(c) Express this as a percentage of her original investment.

Answer 1

#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 (2544.2)/(12000)* 100`

`\\ \rm\Rrightarrow 21.2\%`

Answer 2

(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.)

Explanation:

Simple interest formula

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%

Part (a)

Year 1

⇒ A = 12000(1 + 0.045)

⇒ A = £12,540

Year 2

⇒ A = 12540(1 + 0.05)

⇒ A = £13,167

Year 3

⇒ A = 13167(1 + 0.053)

⇒ A = 13964.851

⇒ A = £13,964.85

Year 4

⇒ A = 13964.851(1 + 0.049)

⇒ A = 14544.2287

⇒ A = £14,544.23

Part (b)

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

Part (c)

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