Answer:
It will take Jacob 36 years to reach his goal
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