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
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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):
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.
