Respuesta :
Answer:
£6911 is the smallest amount Cynthia should invest to get £8000 after three years
Step-by-step explanation:
lets Assume that amount needs to invested for three years = £ x
Rate of Interest = R = 5% per year
Duration in years = n = 3 year
Amount expected after three years when compounded annually = A = £8000
Formula for Amount of compound interest annually is a follows
A = P( 1 + R/100)^n
In our case Principal P = x , Amount A = 8000 , R = 5% and n = 3( since compounded annually). On substituting these values in above formula we get
8000 = x ( 1 + 5/100)^3
⇒8000 = x ( 105/100)^3
⇒8000 = x ( 21/20 )^3
⇒(8000 × 20 × 20 × 20)/(21×21×21) = x
⇒x = 6910.70≈6911
Hence £6911 is the smallest amount Cynthia should invest to get £8000 after three years
Compound interest is the moderated form simple interest. Thus, £6911 is the smallest amount Cynthia should invest to get £8000 after three years.
Principal amount that is invested for three years = £x (Assumption)
Rate of Interest (r) = 5% per year
Duration in years (n) = 3 years
Amount expected after three years when compounded annually (A) = £8000
The formulated way to represent the compound interest is given below:
[tex]A = P( 1 + \dfrac{r}{100})^n[/tex]
In our case Principal P = x , Amount A = 8000 , R = 5% and n = 3 (since compounded annually). On substituting these values in above formula we get
[tex]8000 = x ( 1 + 5/100)^3\\8000 = x ( 105/100)^3\\8000 = x ( 21/20 )^3\\(8000 \times 20 \times 20 \times 20) (21 \times 21 \times 21) = x\\x = 6910.70 \\x=6911[/tex]
Hence, £6911 is the smallest amount Cynthia should invest to get £8000 after three years.
To know more about compound interest, please refer to the link:
https://brainly.com/question/22803385
