SOLUTION: How much should be invested each year for 10 years to provide you with $4000 per year for the next 15 years? Assume a 4.6% interest rate. (Round your final answer to two decimal pl

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Question 1131692: How much should be invested each year for 10 years to provide you with $4000 per year for the next 15 years? Assume a 4.6% interest rate. (Round your final answer to two decimal places.)
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Simple interest formula
+I+=+P%2Ar%2At+
+4000%2A15+=+60000+
+I+%2B+P+=+60000+
+60000%2F10+=+6000+ is +I+%2B+P+
for each year
+P%2Ar%2At+%2B+P+=+6000+
+P%2A%28+.046+%2B+1+%29+=+6000+
+P+=+6000%2F1.046+
+P+=+5736.14+
$5,736.14 must be invested each year
for 10 yrs
-------------------
check:
+I+=+6000+-+5736.14+=+263.86. interest
earned for 1 year
+10%2AI+-+2638.60+
+10%2AP+=+57361.40+
+2638.60+%2B+57361.40+=+60000+
OK
Get a 2nd opinion if needed

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!

How much should be invested each year for 10 years to provide you with $4000 per year for the next 15 years? Assume a 4.6% interest rate. (Round your final answer to two decimal places.)
You DIDN'T state a compounding period. You need to if you want a correct answer.

Assuming it's compounded annually, you'll need highlight_green%28%22%2442%2C664.36%22%29 to withdraw $4,000 per year for 15 years, at an annual interest rate of 4.6%.

To acquire this $42,664.36, you'll need to invest highlight_green%28matrix%281%2C3%2C+%22%243%2C455.85%22%2C+per%2C+year%29%29 for 10 years, at an annual interest rate of 4.6%.	

In other words, you start today and deposit $3,455.85 every year for 10 years. After 10 years you will have $42,664.36, and you'll have

enough to withdraw $4,000 per year for 25 years after that, at 4.6% annual interest rate.



JOSMICELI is doing these types of problems WRONG!

The FORMER calculation is based on AMORTIZATION, while the LATTER involves finding the PAYMENT based on a FUTURE VALUE of an ORDINARY annuity amount.