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)`

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 =
`(r)/(12)`

Time = 12 t [ 1 year = 12 months ]

As r = 0.13 , so rate =
`(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)`