Question

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.

Answer 1

Answer:

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 × $(1+\dfrac{\textrm r}{100})^{\textrm 5}$

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