Question

Find the annual rate of interest. Principal = 4600 rupees Period = 5 years Total amount = 6440 rupees Annual rate of interest = %

Answer 1

Annual rate of interest is 8%.

Answer 2

The rate of interest for compounded annually is 6.96 % .

Explanation:

Given as :

The principal amount = Rs 4600

The time period = 5 years

The amount after 5 years = Rs 6440

Let The rate of interest = R %

From compounded method

Amount = Principal ×
`(1+(\textrm rate)/(100))^(\textrm Time)`

or, Rs 6440 = Rs 4600 ×
`(1+(\textrm R)/(100))^(\textrm 5)`

Or,
`(6440)/(4600)` =
`(1+(\textrm R)/(100))^(\textrm 5)`

or, 1.4 =
`(1+(\textrm R)/(100))^(\textrm 5)`

Or,
`(1.4)^{(1)/(5)}` = 1 +
`(R)/(100)`

or, 1.0696 = 1 +
`(R)/(100)`

or,
`(R)/(100)` = 1.0696 - 1

Or,
`(R)/(100)` = 0.0696

∴ R = 0.0696 × 100

I.e R = 6.96

Hence The rate of interest for compounded annually is 6.96 % . Answer