You invest 5000 in an account earning 4% interest compounded quarterly. How much will you have in 5 years.?
Answers
Answer #1 | 19/12 2013 21:00
Your answer of $5,203 is the amount of the account value after 1 year. After 5 years it is $6,101, based on the formula:
FV = P(1 + r/n)^nt = 5,000 (1.01)^20 = 5,000*1.2201892 = 6.100.95
http://www.moneychimp.com/articles/finworks/contin uous_compounding.htm
Positive: 60 %
Answer #2 | 21/12 2013 05:15
FV = PV(1 + periodic r)^n
periodic r = 0.04 / 4 qtrs. per year = 0.01
n = 5 yrs * 4 qtrs. per year = 20
FV = 5,000(1.01^20)
= 5,000(1.22019)
= $6,100.95
Your teacher's answer is messed up. With his/her answer you're only getting $203 of interest.
203 / 5000 = 0.0406, or 4.06% and only for ONE year.
With 4.06% as the compound equivalent rate, the annual stated rate would be:
((1.0406^1/4) - 1) * 4 = 0.04, or 4%, again, with only one year of interest accruing
over the 5 year period...20 qtrs., the teaching is using...
FV = PV(1 + x)^n
5203 = 5000(1 + x)^20
5203/5000 = (1 + x)^20
1.0406 = (1 + x)^20
1.0406^1/20 = 1 + x
1.00199 = 1 + x
x = 0.00199 for the quarterly rate
x * 4 = stated annual rate = 0.00797, or 0.797%
OR, if the teacher had used the proper rate but messed up on the original deposit...
5203 = PV(1.0125^20)
5203 = PV(1.28204)
5203/1.28204 = PV
PV = $4058.38 (rounded) initial deposit
OK, probably TMI. Teachers are fallible, but that doesn't help when you're ripping your hair out trying to get to their incorrect "correct" answer.
I'll bet your teacher doesn't know how s/he got that answer either.
Positive: 54 %
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