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.

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 ×

Or, = p ×

Or,    = $10,000 ×

Or,    = $10,000 ×

Or,    = $10,000 × 1.11060

Or,   = $11,106

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

For Bank B , at compounded annually

Amount = Principal ×

Or, = p ×

Or,    = $10,000 ×

Or,   = $10,000 ×

So, The Amount in bank B after 5 years =    = $10,000 ×

Now, According to question

The Amount saving in both the banks are equal

i.e =

Or, $11,106 = $10,000 ×

Or, =

Or, 1.1106 =   = 1 +

Or, 1.02120 = 1 +

Or, 1.02120 - 1 =

Or, 0.0212 =  

∴ 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

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step-by-step explanation: