Find the final amount of money in an account if $9,300$ Is deposited at
5% interest compounded semi-annually and the money is left for 10 years.
The final amount is $
Round answer to 2 decimal places
What’s the answer?
Why do you ask for the answer, when all you have to do is apply the formula?
A = P(1 + r/n)^(nt)
For this problem,
A = 9300(1 + .05/2)^(2*10) = _____
Well, let's grab our clown calculators and crunch some numbers, shall we?
To calculate the final amount of money, we'll be using the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = Principal amount (initial deposit)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
In this case:
P = $9,300
r = 5% = 0.05
n = 2 (semi-annually compounded)
t = 10 years
Plugging in the values, we get:
A = 9,300(1 + 0.05/2)^(2*10)
Now excuse me while I grab my clown abacus...
*clownishly calculating intensifies*
*ding*
The final amount, after all the clown calculations, is approximately $15,091.89.
So, my friend, your account will be laughing all the way to the bank with a final amount of $15,091.89!
To find the final amount of money in the account, we can use the formula for calculating compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial deposit) = $9,300
r = annual interest rate (as a decimal) = 5% = 0.05
n = number of times interest is compounded per year (since it's compounded semi-annually, n = 2)
t = number of years = 10
Substituting the given values into the formula:
A = 9300(1 + 0.05/2)^(2*10)
A = 9300(1 + 0.025)^(20)
Using a calculator or spreadsheet, we can calculate:
A ≈ $14,414.16
Therefore, the final amount of money in the account is approximately $14,414.16.
To find the final amount of money in the account, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A is the final amount
P is the principal amount (initial deposit)
r is the interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the number of years
In this case:
P = $9,300
r = 5%/100 = 0.05
n = 2 (since interest is compounded semi-annually)
t = 10 years
Plugging in these values into the formula, we get:
A = 9300(1 + 0.05/2)^(2*10)
Calculating the exponent first, we have:
A = 9300(1.025)^(20)
Using a calculator, we find:
A ≈ $15116.65
Therefore, the final amount of money in the account after 10 years with a $9,300 initial deposit and 5% interest compounded semi-annually is approximately $15,116.65.