Question

An investment of $500 earns interest at an annual interest rate of 13%. The equation for this investment is B = 500(1.13)t, where B represents the balance and t is the number of years. Write an equivalent equation that displays the effective monthly interest rate. A) B = 500(1.10)12t B) B = 500(1.12)12t C) B = 500(1.010)12t D) B = 500(1.012)12t

Answer 1

Answer: C) $B= 500(1.101)^{12t}$

Step-by-step explanation:

Given : The equation for this investment is B = 500(1.13)t, where B represents the balance and t is the number of years.

For monthly interest , Rate = $\dfrac{r}{12}$

Time = 12 t  [ 1 year = 12 months ]

As r = 0.13 , so rate = $\dfrac{0.13}{12}\approx0.010$

Now, the equation will be :

$B=500 (1+0.101)^{12t}$

$\Rightarrow\ B= 500(1.101)^{12t}$

Correct option : C) $B= 500(1.101)^{12t}$