SOLUTION: If 27600 dollars is invested at an interest rate of 10 percent per year, find the value of the investment at the end of 5 years for the following compounding methods. Annual:?

Click here to see ALL problems on Equations

Question 1100043: If 27600 dollars is invested at an interest rate of 10 percent per year, find the value of the investment at the end of 5 years for the following compounding methods.
Annual:?
Semiannual:?
Monthly:?
Daily:?
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
the formula is f = p * (1+r)^n

f is the future value
p is the present value
r is the interest rate per time period.
n is the number of time periods.

Annual:?

the time periods are in years.
annual interest rate = 10% / 100 = .1 / 1 = .1per year.
number of years = 5 / 1 = 5
formula becomes f = 27600 * (1.10)^5 = 44450.08

Semiannual:?

the time periods are in half years.
annual interest rate divided by 10% / 100 = .10 / 2 = .05 per half year.
number of half years = 5 * 2 = 10
formula becomes f = 27600 * (1.05)^10 = 440957.49

Monthly:?

the time periods are in months.
annual interest rate divided by 12 = 10% / 100 = .1 / 12 = .008333333 per month.
number of months = 5 * 12 = 60
formula becomes f = 27600 * (1.008333333)^60 = 45410.53

Daily:?

the time periods are in days.
annual interest rate divided by 365 = 10% / 100 = .1 / 365 = .0002739726 per day.
number of days = 5 * 365 = 1825
formula becomes f = 27600 * (1.0002739726)^1825 = 45501.59

the more the compounding periods per year, the higher the future value.

the formula can also be shown as:

f = p * (1 + r/c) ^ (n*c)

f is the future value
p is the present value
r is the interest rate per year (not the percent).
c is the number of compounding periods per year.
n is the number of years.

in the formulas above, r was already changed to be equal to r/c, and n was already changed to be equal to n*c.

this last formula does it at the time the formula is used.