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

Answer:

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

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

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

Or, $6000 = $4000 × $(1+\dfrac{\textrm r}{100})^{\textrm 15}$

or, $\dfrac{6000}{4000}$ = $(1+\dfrac{\textrm r}{100})^{\textrm 15}$

Or, $\frac{3}{2}$ = $(1+\dfrac{\textrm r}{100})^{\textrm 15}$

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

or, $1.5^{\frac{1}{15}}$ = $(1+\dfrac{\textrm r}{100})$

or, 1.0275 =  $(1+\dfrac{\textrm r}{100})$

or, 1.0275 - 1 = $\dfrac{r}{100}$

or, 0.0275 = $\dfrac{r}{100}$

∴ 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