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

The rate of interest given by bank B is 2.12%

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+(\textrm rate)/(12* 100))^(12* \textrm time)`

Or,
`A_1` = p ×
`(1+(\textrm 2.1)/(12* 100))^(12* \textrm 5)`

Or,
`A_1` = $10,000 ×
`(1+(\textrm 2.1)/(12* 100))^(12* \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+(\textrm rate)/(100))^( \textrm time)`

Or,
`A_2` = p ×
`(1+(\textrm r)/(100))^(\textrm 5)`

Or,
`A_2` = $10,000 ×
`(1+(\textrm r)/(100))^(\textrm 5)`

Or,
`A_2` = $10,000 ×
`(1+(\textrm r)/(100))^(\textrm 5)`

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

Or,
`(11,106)/(10000)` =
`(1+(\textrm r)/(100))^(\textrm 5)`

Or, 1.1106 =
`(1+(\textrm r)/(100))^(\textrm 5)</p><p>Or, , [tex](1.1106)^{(1)/(5)}` = 1 +
`(r)/(100)`

Or, 1.02120 = 1 +
`(r)/(100)`

Or, 1.02120 - 1 =
`(r)/(100)`

Or, 0.0212 =
`(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