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

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

$\\ \rm\Rrightarrow 21.2\%$

Answer 2

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:

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)

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