Question

Bentley is going to invest $98,000 and leave it in an account for 7 years. Assuming

the interest is compounded daily, what interest rate, to the nearest tenth of a percent,
would be required in order for Bentley to end up with $114,000?​

Answer 1

The rate of interest for compounded daily is 2.1 6

Explanation:

Given as :

The principal investment = $ 98,000

The Time period for investment = 7 years

Let The rate of interest compounded daily = R %

The Amount at the end up = $ 114,000

From compounded method

Amount = Principal ×
`(1+(rate)/(365* 100))^(365* Time)`

Or, $ 114,000 = $ 98,000 ×
`(1+(R)/(365* 100))^(365* 7)`

Or,
`(114000)/(98000)` =
`(1+(R)/(36500))^(2555)`

or, 1.16326 =
`(1+(R)/(36500))^(2555)`

or,
`(1.16326)^{(1)/(2555)}` = 1 +
`(R)/(36500)`

1.00005919 - 1 =
`(R)/(36500)`

or, 0.00005919 =
`(R)/(36500)`

∴ R = 0.00005919 × 365000 = 2.16

Hence the rate of interest for compounded daily is 2.1 6 Answer