Question

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

Answer 1

Answer:

The rate of interest for the investment is 4.7%

Step-by-step 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 × $(1+\dfrac{\textrm rate}{100})^{\textrm time}$

∵ Interest = Amount - Principal

So, I = A - p

Or, A = I + p

Or, A = $250 + $3500

i.e A = $3750

∴ A = p × $(1+\dfrac{\textrm r}{100})^{\textrm t}$

Or, $3750 = $3500 × $(1+\dfrac{\textrm r}{100})^{\textrm 1.5}$

Or, $\dfrac{3750}{3500}$ =  $(1+\dfrac{\textrm r}{100})^{\textrm 1.5}$

Or, 1.071428 =  $(1+\dfrac{\textrm r}{100})^{\textrm 1.5}Or, [tex](1.071428)^{\frac{1}{1.5}}$ = $(1 + \dfrac{r}{100})$

Or, 1.047069 = $(1 + \dfrac{r}{100})$

Or, 1.047069 - 1 = $\dfrac{r}{100}$

Or, 0.047069 =  $\dfrac{r}{100}$

∴ 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