Mathematics, 30.12.2019 12:31 zoey1223

Bank a pays an interest rate of 2.1% compounded monthly.
bank b pays an interest rate of r% compounded yearly.
mr tan invests $10 000 in each bank.
after 5 years, his savings in bank a and bank b are equal.
find the value of r.

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Answer from: kaileyy06

The rate of interest given by bank B is 2.12%

Step-by-step explanation:

Given as

The rate of interest given by bank A = 2.1% compounded monthly

The rate of interest given by bank B = r% compounded yearly

The principal invested in each bank are equal = p = $10,000

The time period of investment = t = 5 years

Now, From Compound Interest method

For Bank A , at compounded monthly

Amount = Principal × $(1+\dfrac{\textrm rate}{12\times 100})^{12\times \textrm time}$

Or, A_1 = p × $(1+\dfrac{\textrm 2.1}{12\times 100})^{12\times \textrm 5}$

Or, A_1 = $10,000 × $(1+\dfrac{\textrm 2.1}{12\times 100})^{12\times \textrm 5}$

Or, A_1 = $10,000 × $(1.00175)^{60}$

Or, A_1 = $10,000 × 1.11060

Or, A_1 = $11,106

So, The Amount in bank A after 5 years = A_1 = $11,106

For Bank B , at compounded annually

Amount = Principal × $(1+\dfrac{\textrm rate}{100})^{ \textrm time}$

Or, A_2 = p × $(1+\dfrac{\textrm r}{100})^{\textrm 5}$

Or, A_2 = $10,000 × $(1+\dfrac{\textrm r}{100})^{\textrm 5}$

So, The Amount in bank B after 5 years = A_2 = $10,000 × $(1+\dfrac{\textrm r}{100})^{\textrm 5}$

Now, According to question

The Amount saving in both the banks are equal

i.e A_1 = A_2

Or, $11,106 = $10,000 × $(1+\dfrac{\textrm r}{100})^{\textrm 5}$

Or, $\dfrac{11,106}{10000}$ = $(1+\dfrac{\textrm r}{100})^{\textrm 5}$

Or, 1.1106 = $(1+\dfrac{\textrm r}{100})^{\textrm 5}Or, , [tex](1.1106)^{\frac{1}{5}}$ = 1 + $\dfrac{r}{100}$

Or, 1.02120 = 1 + $\dfrac{r}{100}$

Or, 1.02120 - 1 = $\dfrac{r}{100}$

Or, 0.0212 = $\dfrac{r}{100}$

∴ r = 100 × 0.0210

i.e r = 2.12%

So, The rate of interest given by bank B = r = 2.12%

Hence,The rate of interest given by bank B is 2.12% Answer

Answer from: Quest

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction: this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology: the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion: the last is the discussion, this can be either by management people or persons who are all interested , etc.

Answer from: Quest

It is 198,87032,750 + 375 = 33145 so, we take the 6% and we make it a decimal (0.6) and multiply that, then that is your answer