What is the compound amount and compound interest of $15,000 invested at 6% compounded quarterly for 27 months?
P = Po(1+r)^n.
Po = $15000.
r = (6%/4) / 100% = 0.015 = Quarterly %
rate expressed as a decimal.
n = 4Comp/12mo. * 27mo = 9 Compounding
periods.
Plug the above values into the given Eq
and get:
P = $17,150.85
I = P-Po
Well, if you're looking for the compound amount and compound interest, allow me to calculate it for you with a dash of humor!
So, for $15,000 invested at 6% compounded quarterly for 27 months, you'll end up with a compound amount that will make your piggy bank jump with joy! The compound amount will be approximately $16,750.03.
And what about the compound interest? Well, it's like the cherry on top of your financial cake! The compound interest will be around $1,750.03, giving you a reason to smile at your growing wealth.
Just remember, numbers may be serious, but a little humor along the way never hurts!
To find the compound amount, we can use the formula:
A = P(1 + r/n)^(nt)
where:
A = compound amount
P = principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
Given:
P = $15,000
r = 6% or 0.06 (as a decimal)
n = 4 (quarterly compounding)
t = 27/12 = 2.25 years (since we are given months)
Let's plug in the values into the formula:
A = 15000(1 + 0.06/4)^(4*2.25)
A = 15000(1 + 0.015)^(9)
Now, we can calculate A:
A = 15000(1.015)^9
A ≈ 15000(1.139628757)
A ≈ $17,094.43
Therefore, the compound amount is approximately $17,094.43.
To find the compound interest, we can subtract the principal amount from the compound amount:
Compound interest = Compound amount - Principal amount
Compound interest = $17,094.43 - $15,000
Compound interest ≈ $2,094.43
So, the compound interest is approximately $2,094.43.
To calculate the compound amount and compound interest, we need to use the formula:
Compound Amount = Principal Amount x (1 + Rate/Number of Compounds)^Number of Compounds x Time
Compound Interest = Compound Amount - Principal Amount
In this case, the principal amount is $15,000, the interest rate is 6%, and it is compounded quarterly for 27 months.
Step 1: Convert the time period from months to quarters.
Since compounding is done quarterly, we need to convert 27 months to quarters. There are 12 months in a year, so 27 months is equal to 27/3 = 9 quarters.
Step 2: Calculate the compound amount.
Using the formula, we have:
Compound Amount = $15,000 x (1 + 0.06/4)^4*9
Step 3: Calculate the compound interest.
To find the compound interest, we deduct the principal amount from the compound amount:
Compound Interest = Compound Amount - Principal Amount
Now, let's solve the calculations.
Step 1: Convert the time period from months to quarters.
27 months = 9 quarters
Step 2: Calculate the compound amount.
$15,000 x (1 + 0.06/4)^4*9 = $16,056.50 (rounded to two decimal places)
Step 3: Calculate the compound interest.
Compound Interest = $16,056.50 - $15,000 = $1,056.50
Therefore, the compound amount is approximately $16,056.50, and the compound interest is approximately $1,056.50.