Question

John borrows 2500 from his dad who feels it is best to charge him interest. Six months later, John repays him dad the loan plus interest a total of 2588. What was the annual interest rate on the loan?

Answer 1

6.92%

Explanation:

Using the equation 2,588 = 2,500e0.5r

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Answer 2

7.04%.

Explanation:

We have been given that John borrows 2500 from his dad who feels it is best to charge him interest. Six months later, John repays him dad the loan plus interest a total of 2588.

To find the annual interest rate, we will use simple interest formula.

`A=P(1+rt)`, where,

A = Amount after t years,

P = Principal amount,

r = Annual interest rate,

t = Time in years.

Let us convert our given time in years.

1 year = 12 months

`\text{ 6 months}=\text{0.5 year}`

Upon substituting our given values in above formula, we will get:

`2588=2500(1+r*0.5)`

`2588=2500+1250r`

`2588-2500=2500-2500+1250r`

`88=1250r`

Switch sides:

`1250r=88`

`(1250r)/(1250)=(88)/(1250)`

`r=0.0704`

Now, we will convert our given rate in percentage by multiplying by 100.

`0.0704* 100\%=7.04\%`

Therefore, the annual interest rate on the loan is 7.04%.