SOLUTION: 1. Ellen has $8000 to invest in an RESP (Registered Education Savings Plan) for 7 years. Should she invest her $8000 at 6% compounded semi-annually or should she invest her $8000 a

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: 1. Ellen has $8000 to invest in an RESP (Registered Education Savings Plan) for 7 years. Should she invest her $8000 at 6% compounded semi-annually or should she invest her $8000 a      Log On

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Question 1046232: 1. Ellen has $8000 to invest in an RESP (Registered Education Savings Plan) for 7 years. Should she invest her $8000 at 6% compounded semi-annually or should she invest her $8000 at 7.5% with simple interest? Explain your choice. Identify the function, in each case.
2.Adam is saving for a down payment on a house. How much must he invest now, in one lump sum, in order to have $20 000 at the end of 5 years? Assume the annual interest rate 6.25% compounded monthly.
3. Determine the time it takes to double an investment in an account that pays interest of 4% per annum, compounded quarterly.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1)
Formula for compound interest:
+A+=+P%2A%28+1+%2B+r%2Fn+%29%5E%28n%2At%29+
+P+=+8000+
+r+=+.06+
+n+=+2+
+t+=+7+
-----------------
+A+=+8000%2A%28+1+%2B+.06%2F2+%29%5E%28+2%2A7+%29+
+A+=+8000%2A%28+1.03+%29%5E14+
+A+=+8000%2A1.51259+
+A+=+12100.72+
---------------------------
Formula for simple interest:
+A+=+P%2A%28+1+%2B+r%2At+%29+
+A+=+8000%2A%28+1+%2B+.075%2A7+%29+
+A+=+8000%2A%28+1+%2B+.525+%29+
+A+=+12200+
-------------------
The investment at 7.5% simple interest
gives her more return
+12200+-+12100.72+=+99.28+ more in 7 yrs
---------------------
(2)
+A+=+P%2A%28+1+%2B+r%2Fn+%29%5E%28n%2At%29+
+A+=+20000+
+r+=+.0625+
+n+=+12+
+t+=+5+
+20000+=+P%2A%28+1+%2B+.0625%2F12+%29%5E%2812%2A5%29+
+20000+=+P%2A%28+1+%2B+.005208+%29%5E60+
+20000+=+P%2A1.36573+
+P+=+14644.18+
she should invest $14,644.18 now
--------------------------------
(3)
+A+=+P%2A%28+1+%2B+r%2Fn+%29%5E%28n%2At%29+
+A+=+2P+
+r+=+.04+
+n+=+4+
+2P+=+P%2A%28+1+%2B+.04%2F4+%29%5E%284t%29+
+2+=+%28+1+%2B+.01+%29%5E%284t%29+
Take the log base 10 of both sides
+log%282%29+=+4t%2Alog%28+1.01+%29+
+.301+=+4t%2A.004321+
+.301+=+.017285t+
+t+=+17.413+
+.413%2A12+=+4.96+
it will take about 17 yrs and 5 months
to double an investment
-------------------------
check answer:
+2+=+%28+1+%2B+.01+%29%5E%284t%29+
+2+=+1.01+%5E%284%2A17.413%29+
+2+=+1.01%5E69.652+
+2+=+1.99983+
close enough