Question

BUILD PERSEVERANCE The formula A = P(1 + r) represents the amount of money A in an account after t years, where P is the amount initially deposited and r is the interest rate. Patricia currently has $1839.79 in an account that has an interest rate of 2.5%. She opened the account 8 years ago and has made no additional deposits since then. a. Solve the formula for P and find the amount of Patricia's initial deposit. b. Nia says that for the formula in part a, A is always greater than P when ris positive and t is a positive integer. Do you agree? Why or why not?​

Answer 1

The solution for P is P = A / (1 + r)^t, the initial deposit is $1,510, and I agree that A is always greater than P when given the conditions stated.

How do we calculate the initial deposit?

The correct formula in the question is provided as follows:

A = P(1 + r)^t ........................ (1)

a. P can be solved for and the amount of Patricia's initial deposit can be found from equation (1) as follows:

P = A / (1 + r)^t ................................. (2)

Where:

A = $1839.79

r = 2.5% = 0.025

t = 8

Substituting all the relevant values into equation (2), we have:

P = $1839.79 / (1 + 0.025)^8

P = $1,510

b. Yes, I agree.

The reason is that interest at the rate of 2.5% will be earned yearly on P and added to A making A always greater than P.

Learn more about initial deposits here: brainly.com/question/21845455.

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