Calculate the interest amount of a $4,300 investment for a period of 20 years with a compound interest rate of 3.7% compounded quarterly.
To calculate the interest amount for a compound interest investment, we 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 (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for
In this case,
P = $4,300
r = 3.7% = 0.037 (decimal form)
n = 4 (quarterly compounding)
t = 20 years
Plugging these values into the formula, we have:
A = 4300(1 + 0.037/4)^(4*20)
= 4300(1 + 0.00925)^(80)
= 4300(1.00925)^(80)
≈ 4300(2.20773761)
≈ $9,495.58
To find the interest amount, we subtract the initial principal investment from the future value:
Interest Amount = A - P
= $9,495.58 - $4,300
≈ $5,195.58
Therefore, the interest amount of a $4,300 investment for a period of 20 years with a compound interest rate of 3.7% compounded quarterly is approximately $5,195.58.
wrong
Apologies for the mistake. Let's recalculate:
The compound interest formula for calculating the amount A is:
A = P(1 + r/n)^(nt)
Where:
P = $4,300 (principal investment amount)
r = 3.7% = 0.037 (annual interest rate in decimal form)
n = 4 (quarterly compounding)
t = 20 years
Let's substitute these values into the formula:
A = 4300(1 + 0.037/4)^(4*20)
= 4300(1 + 0.00925)^(80)
= 4300(1.00925)^(80)
≈ 4300(2.208040559)
≈ $9,499.74
To find the interest amount, we subtract the principal investment amount from the future value:
Interest Amount = A - P
= $9,499.74 - $4,300
≈ $5,199.74
Therefore, the interest amount of a $4,300 investment for a period of 20 years with a compound interest rate of 3.7% compounded quarterly is approximately $5,199.74.
Calculate the interest amount of a $4,300 investment for a period of 20 years with a compound interest rate of 3.7% compounded quarterly.
a. $8,981.92
b. $4,712.18
c. $4,681.92
d. $4,702.27
To calculate the interest amount, we can use the formula for compound interest:
A = P(1+r/n)^(nt)
Where:
A = final amount
P = principal amount
r = interest rate per period (in decimal form)
n = number of compounding periods per year
t = number of years
In this case, we have:
P = $4,300
r = 3.7% = 0.037 (decimal form)
n = 4 (quarterly compounding)
t = 20 years
Using the formula, we can calculate the final amount A:
A = 4300(1+0.037/4)^(4*20)
≈ 4300(1+0.00925)^(80)
≈ 4300(1.00925)^(80)
≈ 4300(2.2127582863)
≈ $9,514.75
The interest amount will be the difference between the final amount A and the principal amount P:
Interest Amount = A - P
= $9,514.75 - $4,300
≈ $5,214.75
Therefore, the interest amount of a $4,300 investment for a period of 20 years with a compound interest rate of 3.7% compounded quarterly is approximately $5,214.75.
None of the options given match this result exactly.
just pick an answer
Apologies for the confusion. Given the options provided, the most accurate answer would be:
c. $4,681.92