Question

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)

Answer 1

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

Answer 2

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!