$3,800 principal earning 2%, compounded quarterly, after 7 years
4,369.52
Pt = Po(r + 1)^n.
r = APR / 4 = 2 / 4 = 0.5% = 0.005 =
Quarterly int. rate expressed as a decimal.
n=7yrs * 4 comp/yr = 28 comp. periods.
Pt = 3800(1.005)^28,
Pt = 3800 * 1.14987261 = $4369.52 = principal after 7 yrs.
Int. = Pt - Po = 4369.52 - 3800 = $569.52
To calculate the future value of an investment with a $3,800 principal earning 2% interest compounded quarterly for 7 years, you can use the formula:
Future Value = Principal * (1 + Interest Rate / Number of Compounds)^(Number of Compounds * Number of Years)
In this case, the principal is $3,800, the interest rate is 2% (or 0.02), and the interest is compounded quarterly. Since there are 4 quarters in a year, the Number of Compounds is 4. The Number of Years is 7.
Plugging these values into the formula, we get:
Future Value = $3,800 * (1 + 0.02 / 4)^(4 * 7)
First, let's simplify the exponent part:
(1 + 0.02 / 4)^(4 * 7) = (1 + 0.005)^(28)
Now, we can calculate the value of the exponent:
(1 + 0.005)^(28) ≈ 1.1166529
Finally, multiply the principal by the value we obtained:
Future Value = $3,800 * 1.1166529
Calculating this, we find that the future value of the investment after 7 years is approximately $4,240.98.
To calculate the compound interest on a principal amount over a given period, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A is the final amount (including principal and interest)
P is the principal amount
r is the annual interest rate as a decimal
n is the number of times interest is compounded per year
t is the number of years
In this case, the principal amount is $3,800, the annual interest rate is 2% (or 0.02 as a decimal), it is compounded quarterly, and the time period is 7 years.
First, we need to calculate the number of compounding periods the interest will be applied over the 7-year period. Since the interest is compounded quarterly, there will be 4 compounding periods each year. Therefore, the total number of periods is:
n = 4 periods/year * 7 years = 28 periods
Now we can plug in the values into the formula:
A = 3800(1 + 0.02/4)^(4*7)
Calculating the exponent first:
(1 + 0.02/4)^(4*7) = (1.005)^28 ≈ 1.161704
Now substitute this value back into the formula:
A = 3800 * 1.161704 ≈ $4,413.29
Therefore, after 7 years, the $3,800 principal amount, earning a 2% interest rate compounded quarterly, will grow to approximately $4,413.29.