A principal of $3500 is invested at 8.5% interest, compounded annually. How many years will it take to accumulate $7000 or more in the account?

Answer 1

7000 ≤ 3500(1 + 0.085)^t

Can you solve for t and answer?

Answer 2

We can start by using the Compounded Interest Formula.

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

A represents the amount of money that you can expect

P is the principal or "starting" amount of money you invest

r is the interest rate

n is the number of times you can expect the interest to compound per year

t is the number of periods that have passed.

This question is tricky for a number of reasons, so if you are nervous that is okay!

Our goal is find the number of years to accumulate $7000 what this means in practice is that we will attempt to rewrite the above formula into one that allows us to single out the variable of t given the amount of money we expect to have. the following steps will be numbered to show how the formula has changed.

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

2.A/P=(1+(r/n))^(nt) we divided both sides by P

3.ln(A/P)=ln((1+(r/n))^nt) we raise the entire equation with the natural log 10.

4.ln(A/P)=nt*ln(1+(r/n)) any exponents inside a logarithmic expression can be rewritten as log(a^b)=b*log(a)

5.ln(A/P)/(n*ln(1+(r/n))=t we divided both sides by (n*ln(1+(r/n)) lastly we will plug in the numbers provided.

6.ln(7000/3500)/(1*ln(1+(0.085/1))=t

7.ln(2)/ln(1.085)=t

8.t=8.4965 years approximately 8 and half years.