SOLUTION: 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

Question 1050330: 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.
B. If $5000 is invested at at 5% determine the amount in the account after 6 yr.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

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