U4.L1.HW: Exponential Functions: Question 21

Question

Answer each of the following methods. Then explain your answers afterwards.

If 9600 dollars is invested at an interest rate of 9% per year, find the value of the investment at the end of 5 years for the following compounding methods, to the nearest cent.

(a) Annual: $________

(b) Semiannual: $_______

(c) Monthly: $_______

(d) Daily: $________

Answer 1

The formula for compound interest is A = P(1+r/n)^nt where P is the principal/initial value, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

Annual (1 time per year)

A = 9600(1+0.09/1)^1·5

= 9600(1+0.09)⁵

= 9600(1.09)⁵

≈ $14770.79

Semiannual (2 times per year)

A = 9600(1+0.09/2)^2·5

= 9600(1+0.045)¹⁰

= 9600(1.045)¹⁰

≈ $14908.51

Monthly (12 times per year)

A = 9600(1+0.09/12)^12·5

= 9600(1+0.0075)⁶⁰

= 9600(1.0075)⁶⁰

≈ $15030.54

Daily (∼365 times per year)

A = 9600(1+0.09/365)^365·5

≈ $15054.96

Hope this helped!