Question

$4000 is invested in a mutual fund that pays annual interest compounded quarterly for 15 years. What annual interest is needed to reach a value of $6000?​

Answer 1

The interest needed to reach that value of $6000 is 2.75%

Explanation:

Given as :

The principal that invested in mutual fund = p = $4000

The time period = t = 15 years

The Amount after 15 years = A = $6000

Let The interest needed to reach that value = r%

Now, According to question

From Compound Interest method

Amount = principal ×
`(1+(\textrm rate)/(100))^(\textrm time)`

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

Or, $6000 = $4000 ×
`(1+(\textrm r)/(100))^(\textrm 15)`

or,
`(6000)/(4000)` =
`(1+(\textrm r)/(100))^(\textrm 15)`

Or,
`(3)/(2)` =
`(1+(\textrm r)/(100))^(\textrm 15)`

or, 1.5 =
`(1+(\textrm r)/(100))^(\textrm 15)`

or,
`1.5^{(1)/(15)}` =
`(1+(\textrm r)/(100))`

or, 1.0275 =
`(1+(\textrm r)/(100))`

or, 1.0275 - 1 =
`(r)/(100)`

or, 0.0275 =
`(r)/(100)`

∴ r = 0.0275 × 100

I.e r = 2.75

So, The interest needed to reach that value = r = 2.75%

Hence,The interest needed to reach that value of $6000 is 2.75% Answer