The Romascos hope to have $2,000 in 3 years for a down payment on a new pool. They invest $1,000 in an account that pays 8% interest at the end of each year. Will they have enough money at the end of 3 years to meet their goal of a down payment? What is the difference between their compound amount and their goal?

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a. They will have enough money: they are $760 over the goal amount.

b. They will not have enough money; they are $740.29 short.

c. They will not have enough money: they ate $760 short.

d. They will have enough money; they are $740.29 over the goal amount.

(I have tried to figure it out and I get in between answers. so PLEASE EXPLAIN)

The answer is b, let's start to explain it:

at first, the account is 1000$ and in the first year they'll got 8% of the money, so the account will be 1000$+(1000*8/100) = 1000$+ 80 =1080
second year: they'll got 8% of the total money in account so , they'll got 1080*8/100=86.4
the account will be(in the second year) 1080+86.4= 1166.4
in the third year, they'll benefit 8% of the total, so they'll benefit 1166.4*8/100=93.312$
so , the account will be (in the last of the third year) = 1259.712
the goal is to reach 2000$
2000$-1259.712= 740.288$ equivalent the answer B
(email me if you need more help :) kheloufiomarATgmailDotcom

Thank you so much for explaining that! I wasn't getting that answer at all, but I do see ho you get it. Thank you again!

To determine if the Romascos will have enough money at the end of 3 years to meet their goal, we need to calculate the compound amount of their investment.

The compound amount formula is given by:

A = P(1 + r/n)^(nt)

Where:
A = Total Amount
P = Principal Amount (initial investment)
r = Annual Interest Rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years

In this case, the principal amount (P) is $1,000, the annual interest rate (r) is 8% which is equivalent to 0.08, the times interest is compounded per year (n) is 1 since it's compounded annually, and the number of years (t) is 3.

Let's calculate the compound amount:

A = 1,000(1 + 0.08/1)^(1*3)
= 1,000(1 + 0.08)^3
= 1,000(1.08)^3
= 1,000(1.259712)
= 1,259.71

The compound amount after 3 years is $1,259.71.

Now let's determine the difference between the compound amount and their goal:

Difference = Compound Amount - Goal Amount
Difference = $1,259.71 - $2,000
Difference = -$740.29

So, the correct answer is:

b. They will not have enough money; they are $740.29 short.

To determine if the Romascos will have enough money to meet their goal, we need to calculate the compound amount of their investment over the 3-year period.

The formula to calculate compound interest is: A = P(1 + r)^n

Where:
A = the compound amount (the total amount of money at the end of the investment period)
P = the principal amount (the initial investment)
r = the interest rate (expressed as a decimal)
n = the number of compounding periods

In this case, the principal amount (P) is $1,000, the interest rate (r) is 8% (or 0.08 as a decimal), and the number of compounding periods (n) is 3 years.

Plugging these values into the formula, we have:

A = 1000(1 + 0.08)^3

Calculating this, we get:

A = 1000(1.08)^3
A ≈ 1259.71

So, the compound amount of their investment after 3 years is approximately $1,259.71.

Now, we need to check if this amount is enough to meet their goal of $2,000.

The difference between the compound amount and their goal can be calculated by subtracting the goal amount from the compound amount:

Difference = Compound amount - Goal amount
Difference = 1259.71 - 2000
Difference ≈ -740.29

The difference is approximately $-740.29, which means they are short of their goal amount.

Therefore, the correct answer is:

b. They will not have enough money; they are $740.29 short.