Respuesta :
Answer:
£13,110.49
Step-by-step explanation:
The formula for Compound interest is calculated as =
Compound Interest = Total Amount (A) - Principal (P)
Since we have already been given the principal in the question as £200,000
The next step would be to find and calculated the Total amount(A) that would be saved after 4 years using the formula below:
(A) = P( 1 + r/n) ^nt
Where A = Total amount
P = Principal which means the amount you are investing in savings
r = interest rate
n = number of times the interest is compounded( it could be daily, weekly,monthly or annually).
t = number of time periods elapsed.
From the question, for Claire's savings investment, we were given the following values:
P(Principal) = £200 000
r(interest rate) = 1.6% = 0.016
n = for Claire this is annually i.e per year = 1
t = number of time periods elapsed = 4 years
The total amount been saved after 4 years is calculated as:
A = P( 1 + r/n) ^ nt
A = £200,000( 1 + 0.016/1)¹× ⁴
A = £200,000(1.016)⁴
A = £213,110.48991
Approximately, A = £ 213,110.49
The total amount been saved after 4 years = £ 213,110.49
From the question above, we were asked to calculate the total amount of interest Claire would get after 4 years. And we can do that using this formula:
Total Amount = Principal + Compound interest
Therefore, Compound Interest = Total amount - Principal
Where: Total amount = £213,110.49
Principal = £200,000
Compound interest = £213,110.49 - £200,000
Compound interest = £13,110.49
Therefore, the total amount of interest Claire will get at the end of 4 years = £13,110.49
So sorry about the error. The error has been corrected above already. Thank you.
To calculate compound interest we have to find the total amount. The compound is interest is the subtraction of total amount and principal.
The total amount of interest Claire will get at the end of 4 years is £13,110.49.
Given:
The principal amount is [tex]P=\£200 000[/tex]
Rate of interest [tex]r=1.6\% = 0.016[/tex].
Number of times interest is compounded [tex]n=1[/tex]
Time period [tex]t=4 \:\rm year[/tex].
Calculate the total amount been saved after 4 years.
[tex]A = P\left( 1 +\dfrac{ r}{n}\right ) ^ {nt}[/tex]
Substitute the value.
[tex]A=200,000\left(1+\dfrac {0.016}{1}\right )^4\\A=200,000(1.016)^4\\A=213,110.48991\\A\approx \£ 213,110.49[/tex]
Calculate the compound interest.
[tex]\rm Compound\: Interest = Total\: amount - Principal\\\rm Compound\: Interest=\£213,110.49 - \£200,000\\\rm Compound\: Interest= \£13,110.49[/tex]
Thus, the total amount of interest Claire will get at the end of 4 years is £13,110.49.
Learn more about compound interest here:
https://brainly.com/question/14295570
