Question 1050330
problem statement has been reworded below:


Suppose that p dollars in principal is invested in an account that earns compound interest annually and grows to a dollars in t years. The annual interest rate r is given by r = (a/p)^(1/t) - 1. 


A. Determine the annual interest rate if $2000 grows to $2375.37 after 5 yr.


formula to find r is:


r = a/p ^ (1/t) - 1


in this formula:


a = 2375.37
p = 2000
t = 5



formula becomes:


r = (2375.37/2000) ^ (1/5) - 1


use your calculator to solve for r to get r = .0348886624.


B. If $5000 is invested at at 5% determine the amount in the account after 6 yr.


to determine the amount in the account after 5 years, you have to solve for a.


the formula you are given is r = (a/p)^(1/t) - 1


add 1 to both sides of this equation to get 1+r1 = (a/p)^(1/t)


raise both sides of this equation to the power of t to get:


(1+r)^t = a/p


note that ((a/p)^(1/t))^t is equal to (a/p)^(1/t * t) which is equal to (a/p)^1 which is equal to a/p.


multiply both sides of this equation by p to get:


p * (1+r)^t = a.


you are given that:


p = 5000
r = .05
t = 6


formula becomes:


5000 * (1.05)^6 = a


solve for a to get:


a = 5000 * (1.05)^6 = 6700.478203.