SOLUTION: What interest rate would be necessary to obtain ​$6500 in 8 years if ​$5000 is the amount of the original investment and the interest is compounded​ yearly? the interest rat

Algebra.Com
Question 1193733: What interest rate would be necessary to obtain ​$6500 in 8 years if ​$5000 is the amount of the original investment and the interest is compounded​ yearly?
the interest rate needed is ______ %
​(Do not round until the final answer. Then round to the nearest tenth as​ needed.)
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.
What interest rate would be necessary to obtain ​$6500 in 8 years if ​$5000 is the amount of the original investment and the interest is compounded​ yearly?
the interest rate needed is ______ %
​(Do not round until the final answer. Then round to the nearest tenth as​ needed.)
~~~~~~~~~~~~~~~~ 

Use the formula for the future value of an account compounded yearly

    6500 = 


Your task is to determine the unknown rate "r" from this equation.


For it, divide both sides by 5000

     = 

    1.3 = 


take logarithm base 10 of both sides

    log(1.3) = 8*log(1+r)


and express

    log(1+r) =  = 0.014243.


It means that

    1 + r =  = 1.03334,


which implies   r = 0.03334 = 3.334%.    ANSWER


CHECK.    = 6500.04  dollars  (which is close enough to the precise future value of $6500).

Solved.

-------------

To see many similar and different solved problems,  look into this lesson
    - Problems on discretely compound accounts
in this site, and learn the subject from there.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Logarithms".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.


Happy learning (!)




RELATED QUESTIONS

what interest rate would be necessary to obtain $7500 in 4 years if $5000 is the original (answered by Fombitz)
how much money would be in an account after 5 years if an original investment of $6500... (answered by solver91311,lwsshak3)
the formula for the simple interest earned on an investment is I=prt, where I is the... (answered by rfer)
If $5000 is invested at an interest rate of 4% each year, what is the value of the... (answered by stanbon)
find the interest rate needed for $6500 to grow to $10400 in 3 years if interest is... (answered by jim_thompson5910)
If a 2000 dollar investment grows to 5000 dollars in 14 years, with interest compounded... (answered by Theo)
Find the time required for an investment of 5000 dollars to grow to 6500 dollars at an... (answered by ikleyn)
Find the time required for an investment of 5000 dollars to grow to 6500 dollars at an... (answered by ankor@dixie-net.com,MathTherapy)
Please help with this problem. the interest rate "r" required to increase your... (answered by lwsshak3)