If 10200 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, to the nearest cent.

Question

If 10200 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, to the nearest cent.

(a) Annual: $  

(b) Semiannual: $  

(c) Monthly: $  

(d) Daily: $

Answer 1

The formula for the value of the investment after 5 years would be 10200(1 + 0.10/n)⁵ⁿ where n = the number of compounding periods/yr. Ex: n= 12 for monthly compounding; n = 1 for annual. What the formula does is convert the annual rate (APY) into a per-period rate and raises the compounding factor by the total number of interest-generating periods. You'll see (after you do the calculations) that there is a slight benefit to more frequent compounding.

Answer 2

Use the formula A = P (1 + r / n)^(n t), where

P is the principal, i.e., what you're starting with,

r is the annual rate of interest (be sure to convert to decimal form first),

t is the time interval (in years),

n is the number of compound periods in a year (so, for parts (a) through (d), n is 1, 2, 12, 365 respectively), and

A is the final amount.