Question

Find the interest rate for a ​$4000 deposit accumulating to ​$5234.58​, compounded quarterly for 9 years

Answer 1

Answer:

Interest rate = 3%

Step-by-step solution:

The formula to find the amount for the principal P, after n years with annual rate of interest r% compounded quarterly is:

$A=P(1+\frac{r}{4} )^{4n}$

Here, P = 4000, A = 5234.58 and n = 9

Therefore,

$5234.58=4000(1+\frac{r}{4} )^{4(9)}$

$\frac{5234.58}{4000} = (1+\frac{r}{4} )^{36}$

$1.308645 = (1+\frac{r}{4} )^{36}$

$1+\frac{r}{4} =1.308645 ^{\frac{1}{36} }$

$1+\frac{r}{4} =1.0075$

$\frac{r}{4} =1.0075-1$

= 0.0075

r = 0.0075 × 4 = 0.03

= 3%