Find the amount in a account where $200 is invested at 3.5% compounded quarterly for a period of 3 years.

Mathematics

1 answer:

AveGali [126]3 years ago

6 0

Answer:

$222.04

Step-by-step explanation:

Use the compound amount formula A = P(1 + r/n)^(nt), where n is the number of times interest is compounded per year, t is the number of years and r is the interest rate as a decimal fraction.

Here, A = ($200)(1 + 0.035/4)^(4*3), or

= ($200)(1.00875)^(12) = $200(1.11) = $222.04

The compound amout after 4 years (12 compounds) will be $222.04.

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elixir [45]

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Answer:

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b) P(98 < X < 100) = 0.4525

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .