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Diego decided to invest his $500 tax refund rather than spending it. He found a bank that would pay him 4% interest, compounded quarterly. If he deposits the entire $500 and does not deposit or withdraw any other amount, how long will it take him to double his money in the account

 Apr 16, 2014

Best Answer 

 #1
avatar+118608 
+8

I am assuming that you mean 4% per annum, that is 1% or 0.01 per quarter

FV=PV(1+i)n

1000=500(1+0.01)n

2=1.01n

log2 = log1.01n

log2 = nlog1.01

n=log2 / log1.01

n=69.66 quarters

time = 70/4 = 17.5 years

 Apr 17, 2014
 #1
avatar+118608 
+8
Best Answer

I am assuming that you mean 4% per annum, that is 1% or 0.01 per quarter

FV=PV(1+i)n

1000=500(1+0.01)n

2=1.01n

log2 = log1.01n

log2 = nlog1.01

n=log2 / log1.01

n=69.66 quarters

time = 70/4 = 17.5 years

Melody Apr 17, 2014
 #2
avatar+128408 
+5

Thanks for that answer, Melody.....Note something interesting.....The time it takes to double his money under these conditions is independent of what he started with...In other words, it would take him as long to double $1M as it would $500......... ( )

 Apr 17, 2014

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