Exponential Function

Question

If 47000 dollars is invested at an interest rate of 8 percent per year, find the value of the investment at the end of 5 years for the following compounding methods, to the nearest cent.

Annual:

 Semiannual: 

Monthly

Daily:

Answer 1

1.) Determine the correct equation to use:

P = P_°(1+r/n)^nt

where P_° = the principal, r = the rate in decimal form, P = the new balance, n = the number of times it is compounded, t = the time in years

In the following methods, the variable n is the only variable that will change

Annual: n = 1 P = 47,000(1 + 0.08/1)(1 x 5) = 69058.42

Semiannual: n = 2 P = 47,000(1 + 0.08/2)(2 x 5) = 69571.48

Monthly: n = 12 P = 47,000(1 + 0.08/12)(12 x 5) = 70022.75

Daily: n = 360. P = 47,000(1 + 0.08/360)(360 x 5) = 70112.65