a)
solve for x, the original amount
x + 17(.0398)x = 25000
b)
i = .0398/4 = .00995
x(1.00995)^68 = 25000
x = 25000/(1.00995^68) = .......
c)
25000 = x (e^(.0398(17))
x = ...
a. The account pays simple interest
b. the account compound interest qrtly
c. the account compounds interest continuously
solve for x, the original amount
x + 17(.0398)x = 25000
b)
i = .0398/4 = .00995
x(1.00995)^68 = 25000
x = 25000/(1.00995^68) = .......
c)
25000 = x (e^(.0398(17))
x = ...
a. Simple Interest:
The formula for calculating simple interest is:
I = P * r * t
Where:
I = Interest
P = Principal amount (the initial investment)
r = Annual interest rate (expressed as a decimal)
t = Time period in years
To achieve a balance of $25,000 in 17 years, substitute the given information into the formula and solve for P:
25,000 = P * 0.0398 * 17
b. Quarterly Compounding:
The formula for calculating compound interest with quarterly compounding is:
A = P * (1 + r/n)^(n*t)
Where:
A = Final amount (desired balance)
P = Principal amount (the initial investment)
r = Annual interest rate (expressed as a decimal)
n = Compounding frequency per year
t = Time period in years
To achieve a balance of $25,000 in 17 years, substitute the given information into the formula, set A = $25,000, and solve for P:
25,000 = P * (1 + 0.0398/4)^(4*17)
c. Continuous Compounding:
The formula for calculating compound interest with continuous compounding is:
A = P * e^(r*t)
Where:
A = Final amount (desired balance)
P = Principal amount (the initial investment)
r = Annual interest rate (expressed as a decimal)
t = Time period in years
e = Euler's number, approximately 2.718
To achieve a balance of $25,000 in 17 years, substitute the given information into the formula, set A = $25,000, and solve for P:
25,000 = P * e^(0.0398*17)
By solving these equations, you can find out the amount of money that needs to be invested in each scenario to achieve a balance of $25,000 in 17 years.