Question

Find the interest rate that generated $250 in interest for an investment of $3500 after 18 months

Answer 1

The rate of interest for the investment is 4.7%

Explanation:

Given as :

The interest amount for investment = I = $250

The investment amount = p = $3500

The time period for investment = 18 months = 1.5 years

Let The rate of interest applied = r%

Now, From Compound Interest

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

∵ Interest = Amount - Principal

So, I = A - p

Or, A = I + p

Or, A = $250 + $3500

i.e A = $3750

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

Or, $3750 = $3500 ×
`(1+(\textrm r)/(100))^(\textrm 1.5)`

Or,
`(3750)/(3500)` =
`(1+(\textrm r)/(100))^(\textrm 1.5)`

Or, 1.071428 =
`(1+(\textrm r)/(100))^(\textrm 1.5)</p><p>Or, [tex](1.071428)^{(1)/(1.5)}` =
`(1 + (r)/(100))`

Or, 1.047069 =
`(1 + (r)/(100))`

Or, 1.047069 - 1 =
`(r)/(100)`

Or, 0.047069 =
`(r)/(100)`

∴ r = 0.047069 × 100

i.e r = 4.7069

So, The rate of interest = r = 4.7%

Hence, The rate of interest for the investment is 4.7% Answer