Recently, a certain bank offered a 10-year CD that earns 8.93% compounded continuously.
a) If $20,000 is invested in this CD, how much will it be worth in 10 years?
Ans: I used the formula A = Pe^(rt) to get the answer $48,848.92
b)How long will it take for the account to be worth $50,000?
I just need help in solving part b) thank you!
Just solve
20 e^(.0893t) = 50
e^.0893t = 2.5
.0893t = ln(2.5)
t = ln(2.5)/.0893 = 10.26
To solve part b), we need to rearrange the formula A = Pe^(rt) to solve for t (time). In this case, our target amount (A) is $50,000.
The rearranged formula becomes:
t = ln(A/P) / r
where:
- t represents the time in years
- ln denotes the natural logarithm
- A represents the target amount ($50,000 in this case)
- P is the initial principal amount ($20,000 in this case)
- r is the interest rate (8.93% compounded continuously)
Let's substitute these values into the formula:
t = ln($50,000 / $20,000) / 0.0893
Now, we can solve for t using a calculator or computer software with natural logarithm capabilities:
t ≈ ln(2.5) / 0.0893
t ≈ 0.916 / 0.0893
t ≈ 10.24 years
Therefore, it will take approximately 10.24 years for the account to be worth $50,000.