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3 years ago

Claire invests £200 000 in a savings account for 4 years.

Mathematics

1 answer:

Digiron [165]3 years ago

5 0

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.

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o-na [289]

Answer:

(a) The probability of the event (X > 84) is 0.007.

(b) The probability of the event (X < 64) is 0.483.

Step-by-step explanation:

The random variable X follows a Poisson distribution with parameter λ = 64.

The probability mass function of a Poisson distribution is:

$P(X=x)=\frac{e^{-\lambda}\lambda^{x}}{x!};\ x=0, 1, 2, ...$

(a)

Compute the probability of the event (X > 84) as follows:

P (X > 84) = 1 - P (X ≤ 84)

$=1-\sum _{x=0}^{x=84}\frac{e^{-64}(64)^{x}}{x!}\\=1-[e^{-64}\sum _{x=0}^{x=84}\frac{(64)^{x}}{x!}]\\=1-[e^{-64}[\frac{(64)^{0}}{0!}+\frac{(64)^{1}}{1!}+\frac{(64)^{2}}{2!}+...+\frac{(64)^{84}}{84!}]]\\=1-0.99308\\=0.00692\\\approx0.007$

Thus, the probability of the event (X > 84) is 0.007.

(b)

Compute the probability of the event (X < 64) as follows:

P (X < 64) = P (X = 0) + P (X = 1) + P (X = 2) + ... + P (X = 63)

$=\sum _{x=0}^{x=63}\frac{e^{-64}(64)^{x}}{x!}\\=e^{-64}\sum _{x=0}^{x=63}\frac{(64)^{x}}{x!}\\=e^{-64}[\frac{(64)^{0}}{0!}+\frac{(64)^{1}}{1!}+\frac{(64)^{2}}{2!}+...+\frac{(64)^{63}}{63!}]\\=0.48338\\\approx0.483$