Romy invested $5,000 into an account that pays 5% compound semi-annually. He intended to keep the account untouched for five years. However, after three years he had to withdraw $3,000. Find the amount left in the account five years from the time he made his investment.
So you have the three years + what is left at the two years
A=p(1+i)^n for the first three years BUT the rate was given for 5 years
A=5000(1 +.05/2)^3x2
A=5000(1.025)^6
A=5000(1.159693418)
A=5798.85 after the three years...
Then he took out 3000 so the new Principal is 2798.47
using A=p(1+i)^n
You figure out the next 2 years :)
To find the amount left in the account after five years, we need to calculate the future value of the initial investment of $5,000 compounded semi-annually for five years.
Given:
Principal (P) = $5,000
Interest rate (r) = 5% (0.05)
Compounded semi-annually
Time (t) = 5 years
We need to calculate the future value (FV) of the investment after five years.
The formula to calculate future value in compound interest is:
FV = P * (1 + r/n)^(n*t)
Where:
FV = Future Value
P = Principal (Initial investment)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Time in years
In this case, interest is compounded semi-annually, which means it is compounded twice a year. So, n = 2.
Now, let's calculate the future value (FV) after five years.
FV = $5,000 * (1 + 0.05/2)^(2*5)
FV = $5,000 * (1 + 0.025)^(10)
FV = $5,000 * (1.025)^(10)
FV ≈ $5,000 * 1.28008429
The future value is approximately $6,400.42
However, after three years, Romy withdrew $3,000 from the account.
To find the balance remaining in the account after five years, we subtract the withdrawn amount from the future value:
Balance remaining = FV - Withdrawn amount
Balance remaining = $6,400.42 - $3,000
The balance remaining in the account after five years is approximately $3,400.42.