Jacob is unsure how long it will take to save $50,000. He knows that he'll make an initial investment of $5,000, and he can earn 6.5% interest per year, compounded semiannually. How long will it take for Jacob to reach is goal?

It will take Jacob 36 years to reach his goal

Step-by-step explanation:

In this question, Jacob is intending to save $50,000 but he is doing this by saving $5,000 at an interest which is compounded two times a year (semi-annually). We are tasked with calculating the number of years it will take him.

Mathematically, to solve this, what we use is the compound interest formula.

This is;

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

Where in the question A is our savings target of $50,000

P is our initial amount saved of $5,000

r is the rate at 6.5%

n is the number of times interest will be compounded per year= 2

and t is the number of years it will take.

We plug all these values respectively to yield;

50,000 = 5,000(1 + 0.065/2)^(2t)

Divide through by 5,000

we have;

10 = (1.0325)^2t

Take the logarithm of both sides

Log 10 = Log (1.0325)^2t

Log 10 = 2tLog (1.0325)

2t = Log10/Log1.0325

2t = 72

t = 72/2

t = 36 years

$12. that is my answer.