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?
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.
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) = _____