Joe Diamond deposited $9,000 into the Rong Bank that pays 12 percent interest, compounded quarterly. Calculate the amount Joe will have in his account at the end of 4 years. (Using the Calculator)
Pt = Po(1+r)^n.
r = (12%/4)/100% = 0.03 = Quarterly % rate expressed nas a decimal.
n = 4comp/yr * 4yrsw = 16 Compounding
periods.
Pt = 9000(1.03)^16 = $14,442.36
To calculate the amount Joe will have in his account at the end of 4 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount in the account
P = the initial deposit
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case,
P = $9,000
r = 12% = 0.12 (converted to decimal)
n = 4 (compounded quarterly)
t = 4 years
Using the calculator, we can substitute these values into the formula:
A = 9000(1 + 0.12/4)^(4*4)
A ≈ 9000(1 + 0.03)^(16)
Calculating the bracketed term:
(1 + 0.03)^(16) ≈ 1.03^(16)
Using the calculator, we find that 1.03^(16) is approximately 1.634
Substituting this value back into the original equation:
A ≈ 9000 * 1.634
Calculating this final multiplication in the calculator:
A ≈ $14,706.44
Therefore, Joe will have approximately $14,706.44 in his account at the end of 4 years.
To calculate the amount Joe will have in his account at the end of 4 years with compound interest, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the amount of money Joe will have at the end of the 4-year period,
P is the principal amount (the initial deposit) which is $9,000,
r is the annual interest rate expressed as a decimal (12% becomes 0.12),
n is the number of times the interest is compounded per year (quarterly compounding means n = 4),
and t is the number of years.
Let's plug in the values into the formula and calculate:
A = 9000(1 + 0.12/4)^(4*4)
First, divide the annual interest rate by the number of times compounded per year:
0.12/4 = 0.03
Next, calculate the exponent by multiplying the number of times compounded per year by the number of years:
4*4 = 16
Now, let's calculate:
A = 9000(1 + 0.03)^(16)
= 9000(1.03)^(16)
To calculate this expression, you can use a calculator. Simply raise 1.03 to the power of 16 and multiply the result by $9,000. The final value will give you the amount Joe will have in his account at the end of 4 years.
Using a calculator, the result is approximately $13,838.71. Therefore, Joe will have approximately $13,838.71 in his account at the end of 4 years.