Question

A local bank is running the following advertisement in the​ newspaper: "For just $ $2,000 we will pay you $140 ​forever!" The fine print in the ad says that for a $2,000 ​deposit, the bank will pay $140 every year in​ perpetuity, starting one year after the deposit is made. What interest rate is the bank advertising​ (what is the rate of return of this​ investment)?

Answer 1

6.56%

Step-by-step explanation:

Given:

The amount paid to the bank = $2,000

Let the interest rate paid be 'r'

By compound interest ,

After 1 year the paid amount will be $2000 × ( 1 + r )

Now,

the bank is paying $140 every year

thus,

2000 × ( 1 + r ) =
`\frac{\textup{140}}{\textup{r}}`

or

2000r + 2000r² = 140

on solving the above quadratic equation, we get

r = 0.0656

or

r = 6.56%

Hence,

interest rate the bank advertising = 6.56%