Question

1 Jesy invests £8000 for n years in a savings account.
To find the value, V, of her investment after n years she uses the formula:
V = 8000 X (1.025)"
(a) Write down the annual rate of interest Jesy earns.
(b) Find the total amount of interest Jesy earns in three years.​

Answer 1

SOLUTION

GIVEN

Jesy invests £8000 for n years in a savings account.

To find the value, V, of her investment after n years she uses the formula:

$\sf{V = 8000 \times {(1.025)}^{n} }$

TO DETERMINE

(a) Write down the annual rate of interest Jesy earns.

(b) Find the total amount of interest Jesy earns in three years.

EVALUATION

(a)

$\sf{V = 8000 \times {(1.025)}^{n} }$

$\displaystyle\sf{ \implies \: V = 8000 \times {(1 + 0.025)}^{n} }$

$\displaystyle\sf{ \implies \: V = 8000 \times { \bigg(1 + \frac{25}{1000} \bigg)}^{n} }$

$\displaystyle\sf{ \implies \: V = 8000 \times { \bigg(1 + \frac{2.5}{100} \bigg)}^{n} }$

From above we can conclude that

Principal =

Time = n years

Rate of interest = 2.5%

(b) Now we have to find the total amount of interest Jesy earns in three years.

So n = 3

$\displaystyle\sf{ \implies \: V = 8000 \times { \bigg(1 + \frac{2.5}{100} \bigg)}^{3} }$

$\displaystyle\sf{ \implies \: V = 8000 \times { ( 1.025)}^{3} }$

$\displaystyle\sf{ \implies \: V = 8000 \times 1.077 }$

$\displaystyle\sf{ \implies \: V = 8616 }$

Hence the total amount of interest Jesy earns in three years

= £ 8616 - £ 8000

= £ 616

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