Calculate the compound interest on 7400 in 4years at 6% p.a. if interest is calculated every three months
Well, well, well, looks like someone wants to dive into the world of finance! Alright, let's calculate that compound interest for you.
First, we need to figure out how many times interest is being calculated in a year. Since it's being calculated every three months, that means we have 4 interest periods per year (12 months divided by 3).
Next, we need to calculate the interest rate per period. Since the annual interest rate is 6%, we divide it by the number of interest periods in a year. That gives us 1.5% (6% divided by 4).
Now that we have all our numbers, let's calculate the compound interest using the formula:
A = P*(1 + r/n)^(n*t)
Where:
A = Final amount
P = Principal amount (initial investment)
r = Annual interest rate (in decimal form)
n = Number of times interest is compounded per year
t = Number of years
Plugging in the values:
P = $7400
r = 6% = 0.06
n = 4
t = 4
A = 7400 * (1 + 0.06/4)^(4*4)
Doing some math magic, here's the result: $9,180.83.
So, after 4 years at 6% interest compounded quarterly, your $7400 will grow to approximately $9,180.83. That's quite the magical increase, don't you think?
To calculate compound interest on 7400 in 4 years at a 6% interest rate compounded quarterly, we need to use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (7400 in this case)
r = annual interest rate (6% or 0.06 as a decimal)
n = number of times that interest is compounded per year (quarterly = 4)
t = number of years
Let's plug in the given values:
A = 7400(1 + 0.06/4)^(4*4)
Now we can solve it step-by-step:
Step 1: Calculate the interest rate per period
0.06/4 = 0.015
Step 2: Calculate the total number of compounding periods
4 * 4 = 16
Step 3: Calculate the compound interest
A = 7400(1 + 0.015)^16
To calculate this, you can use a calculator or spreadsheet. The result is approximately 9,363.38
Therefore, the compound interest on 7400 in 4 years at a 6% interest rate compounded quarterly is approximately 9,363.38.
To calculate compound interest, you can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (including interest)
P = the principal amount (initial investment)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years
In this case, the principal amount (P) is $7,400, the annual interest rate (r) is 6% or 0.06, the interest is calculated every three months (n = 4 times per year), and the time period (t) is 4 years.
Plugging these values into the formula, we get:
A = 7400(1 + 0.06/4)^(4*4)
A = 7400(1 + 0.015)^16
A = 7400(1.015)^16
Now we can calculate this with a calculator or spreadsheet:
A ≈ 7400 * 1.27198
A ≈ $9,410.24
Therefore, the compound interest on $7,400 over 4 years at an annual interest rate of 6% with interest calculated every three months is approximately $2,010.24.
P = Po(1+r)^n.
Po = $7400
r = 0.06(1/4) = 0.015 = Quarterly % rate.
n = 4comp./yr * 4yrs = 16 compounding periods.
I = P-Po.