Estimate the interest rate necessary for a value of $8500 to grow to $10000 if interest is compounded semiannually for 5 years.

Question

I’m stuck in this question and am not sure how tonfigure out the answer!

Answer 1

you want to use the compound interest formula to set this one up!

A = P(1 + r/n)^(nt)

substituting in the values given to us in the information in the question and then solving that for the value of "r" yields

10000 = 8500(1 + r/2)^(2*5)

1.17647 = (1 + r/2)^10

(1.17647)^(1/10) = 1 + r/2

0.01639 = r/2

r = 0.01639 *2 = 0.03278 x 100% = 3.28%

meaning that you need an interest rate of 3.28% for a value of $8,500 to grow to $10,000 if the interest is compounded semiannually for 5 years

Answer 2

A(t) = P(1+r/n)^nt

 

    P = principal (starting amount)

    r = annual interest rate in decimal form

    n = number of times that interest is compounded per year

    t = number of years

    A(t) = amount in t years

 

So, 10000 = 8500(1+r/2)²⁽⁵⁾

 

 1.1764706 = (1+r/2)¹⁰

 

 1+r/2 = (1.1764706)^1/10

 

 1 + r/2 = 1.01638

 

       r/2 = 0.01638

 

         r = 0.03276 = 3.276%