Question

7100 dollars is placed in an account with an annual interest rate of 5%. To the nearest tenth of a year, how long will it take for the account value to reach 26400 dollars ?

Answer 1

Answer: x=26.9

Explanation:

Answer 2

After
`26.91\ years` the principle amount value will reach to
`26400\ dollars`.

Explanation:

Given that,

Principle Amount
`(P)= 7100\ dollars`

Rate of Interest
`(R)=`
`5`%

Total Amount
`(A)= 26400\ dollars`

If Principle Amount
`(P)`
`=P\ dollars`, Time
`=t\ years`, Rate of Interest
`=R`%
`pa`

when interest is compounded annually:

Total Amount after
`t\ years`
`= P(1+(R)/(100)) ^(t)`

Now,

`A= P(1+(R)/(100)) ^(t)`

⇒
`26400=7100(1+(5)/(100)) ^(t)`

⇒
`3.7183=(1+0.05)^(t)`

⇒
`3.7183=(1.05)^(t)`

taking log both sides, we get

`ln(3.7183)=ln {(1.05)^(t)}`

⇒
`1.31327=t* ln(1.05)`

⇒
`1.31327=t* 0.04879`

⇒
`t=26.91`

Therefore,

After
`26.91\ years` the principle amount value will reach to
`26400\ dollars`.