A is accumulated amount investing after p principal for t years at and interest rate of r compounded anually k is times per year.
P=$1500, r= 7%, t=6
P=1500, r=7%,t=5,k=4
P=$1250, r=5.4%,t=6
I will do the second, then you follow the same method to do the other two
2.
A = 1500(1 + .07/4)^(5*4)
= 1500(1.0175^20
= 2122.17
in the first and third assume that k = 1, that is keep the rate at .07 and .054
To calculate the accumulated amount for the given scenarios, we have to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
- A is the accumulated amount
- P is the principal amount
- r is the annual interest rate (as a decimal)
- t is the number of years
- n is the number of times interest is compounded per year
Let's calculate the accumulated amount for each scenario:
Scenario 1:
P = $1500, r = 7%, t = 6, k = 1 (interest is compounded annually)
n = 1 (compounded annually)
A = 1500(1 + 0.07/1)^(1*6)
A = 1500(1 + 0.07)^6
A = 1500(1.07)^6
A ≈ $2,387.17
Scenario 2:
P = $1500, r = 7%, t = 5, k = 4 (interest is compounded quarterly)
n = 4 (compounded quarterly)
A = 1500(1 + 0.07/4)^(4*5)
A = 1500(1 + 0.0175)^20
A ≈ $2,391.58
Scenario 3:
P = $1250, r = 5.4%, t = 6, k = 1 (interest is compounded annually)
n = 1 (compounded annually)
A = 1250(1 + 0.054/1)^(1*6)
A = 1250(1 + 0.054)^6
A ≈ $1,657.09
Therefore, the accumulated amounts for the given scenarios are approximately:
1. $2,387.17
2. $2,391.58
3. $1,657.09
To calculate the accumulated amount for each scenario, we can use the formula for compound interest:
A = P(1 + r/k)^(kt)
where:
A = accumulated amount
P = principal
r = interest rate
t = number of years
k = number of times interest is compounded per year
Let's solve each scenario step-by-step:
Scenario 1:
P = $1500, r = 7%, t = 6, k is not given
We can substitute the given values into the formula:
A = 1500(1 + 0.07/k)^(6k)
Since the value of k is not provided, we cannot calculate the exact accumulated amount without this information.
Scenario 2:
P = $1500, r = 7%, t = 5, k = 4
Substituting the given values into the formula:
A = 1500(1 + 0.07/4)^(4*5)
A = 1500(1.0175)^20
A ≈ 1500(1.41051271760)
A ≈ $2,115.77
Therefore, the accumulated amount for Scenario 2 is approximately $2,115.77.
Scenario 3:
P = $1250, r = 5.4%, t = 6, k is not given
Again, we can substitute the given values into the formula:
A = 1250(1 + 0.054/k)^(6k)
Since the value of k is not provided, we cannot calculate the exact accumulated amount without this information.
Note: If k is not given, it is impossible to calculate the accumulated amount precisely without the number of compounding periods per year.