Question

What investment does Patrick need to make at the end of each year into his savings account over the coming 5 years to reach his vacation goal of $10,000 if he is getting 5% APR on his account?

A) $1,600
B) $1,800
C) $2,000
D) $2,200

Answer 1

To reach a $10,000 vacation goal in 5 years with a 5% APR, Patrick needs to make an annual payment of approximately $1,800 into his savings account. The correct answer is option B.

Step-by-step explanation:

Patrick wants to reach a savings goal of $10,000 with an annual contribution to his savings account which has an APR of 5%. To solve this, we can use the formula for the future value of a series of annuities: FV = Pmt * (((1 + r)^n - 1) / r)

Where: Pmt = annual payment, r = annual interest rate (as a decimal) n = number of payments, FV = future value of the investment. We want the future value (FV) to be $10,000, the interest rate (r) is 0.05 (5%), and the number of payments (n) is 5. Plugging these values into the formula, we can solve for Pmt:

$10,000 = Pmt * (((1 + 0.05)^5 - 1) / 0.05). Solving for Pmt gives us an annual payment amount of approximately $1,800. Therefore, the correct answer to Patrick's question is B) $1,800.