Question

2. An initial $1900 investment was worth $2400 after two years and six months. What quarterly compounded nominal rate of return did the investment earn?

Answer 1

The rate of interest compounded quarterly is 9.2%

Step-by-step explanation:

Given as :

Initial investment principal = p = $1900

Amount after 2 years 6 months = A = $2400

Time period = T =  2 years 6 months = 2.5 years

Let The rate of interest compounded quarterly = r%

According to question

From Compound Interest method

Amount = Principal × $(1+\dfrac{rate}{4\times 100})^{4 \times Time}$

i.e  A = p × $(1+\dfrac{r}{4\times 100})^{4 \times T}$

Or, $2400 = $1900 × $(1+\dfrac{r}{4\times 100})^{4 \times 2.5}$

Or, $(1+\dfrac{r}{4\times 100})^{ 10}$ = $\dfrac{2400}{1900}$

Or, $(1+\dfrac{r}{4\times 100})^{ 10}$ = 1.26

Taking power $\dfrac{1}{10}$ both side

$(1+\dfrac{r}{4\times 100})^{}$  =  $(1.26)^{\dfrac{1}{10}}$

or,   $(1+\dfrac{r}{4\times 100})^{}$  = 1.023

Or, $\dfrac{r}{400}$ = 1.023 - 1

Or, $\dfrac{r}{400}$  = 0.023

∴    r = 9.2

So, The rate of interest compounded quarterly = r = 9.2%

Hence, The rate of interest compounded quarterly is 9.2%  Answer