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brooooke19

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Someone, please help me solve this!! (I already determined the first three parts of the equation I'm just having trouble determining the last section) and if you could show me how! Thank you kindly

How much should you invest each month in order to have $400,000 if your rate of return is 3% compounded monthly and you want to achieve your goal in 40 years? How much interest will you earn? How much should you invest each month in order to have $400,000 if you want to achieve your goal in 20 years? *** If you deposit the amount you need to achieve your goal in 20 years, how much will your savings be worth after 10 years?***
 
brooooke19 said:
Someone, please help me solve this!! (I already determined the first three parts of the equation I'm just having trouble determining the last section) and if you could show me how! Thank you kindly

How much should you invest each month in order to have $400,000 if your rate of return is 3% compounded monthly and you want to achieve your goal in 40 years? How much interest will you earn? How much should you invest each month in order to have $400,000 if you want to achieve your goal in 20 years? *** If you deposit the amount you need to achieve your goal in 20 years, how much will your savings be worth after 10 years?***
Click to expand...
Please share your work for the first three parts that you have solved. That will give us an idea about your status in this subject.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem
 
Step 1. How much should you invest each month?
400,000 = PMT ((1+0.03)^(12x40)-1)
(divide both sides)
0.03
12
400,000 = PMT (926.0595012)
(divide both sides)
(926.0595012) (926.0595012)
$431.94 = PMT (monthly deposit for 40 years, rounded to the nearest cent)

Step 2. How much interest will you earn?
$431.94 x 12 x 40 = $207,331.20
$400,000 - $207,331.20 =$192,668.80 (interest earned over 40 years)

Step 3. How much should you deposit monthly to have $400,000 saved in 20 years at 3% compounded monthly?
400,000 = PMT ((1+0.03)^(12x20)-1)
(divide both sides)
0.03
12
400,000 = PMT (328.3019981)
(divide both sides)
(328.3019981) (328.3019981)
$1218.39 = PMT (monthly deposit for 20 years, rounded to the nearest cent)

Step 4. If you deposit the amount you need to achieve your goal in 20 years, how much will your savings be worth after 10 years?

Need help with this step, I don't where to start.
 
brooooke19 said:
Step 1. How much should you invest each month?
400,000 = PMT ((1+0.03)^(12x40)-1)
(divide both sides)
0.03
12
400,000 = PMT (926.0595012)
(divide both sides)
(926.0595012) (926.0595012)
$431.94 = PMT (monthly deposit for 40 years, rounded to the nearest cent)

Step 2. How much interest will you earn?
$431.94 x 12 x 40 = $207,331.20
$400,000 - $207,331.20 =$192,668.80 (interest earned over 40 years)

Step 3. How much should you deposit monthly to have $400,000 saved in 20 years at 3% compounded monthly?
400,000 = PMT ((1+0.03)^(12x20)-1)
(divide both sides)
0.03
12
400,000 = PMT (328.3019981)
(divide both sides)
(328.3019981) (328.3019981)
$1218.39 = PMT (monthly deposit for 20 years, rounded to the nearest cent)

Step 4. If you deposit the amount you need to achieve your goal in 20 years, how much will your savings be worth after 10 years?

Need help with this step, I don't where to start.
Click to expand...
You've determined the monthly payment amount. Accumulate all of the payments to the end of 10 years
or discount the payments made in years 11-20 to the end of year 10.
 
brooooke19 said:
If you deposit the amount you need to achieve your goal in 20 years, how much will your savings be worth after 10 years?
Click to expand...

Is this the exact wording of the question? Please check it carefully, since it doesn't seem very clear to me. I am inclined to agree with BigBeachBanana's interpretation (post#4)

Post#4 assumes that it's another recurring deposit compound interest question, with the same monthly payment amount as the previous question but only running for 10 years instead of 20

However, there is another interpretation... the last question might be a simple interest question. An initial deposit of amount "x" invested for 10 years. And x is the sum of all the monthly payments from the previous question. It's the word deposit that gives me this thought (to me this word implies a single, one time, payment). However, in the context of the rest of the question, this would seem a bit strange. Therefore, I'd probably answer it like post#4 :unsure::)
 
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