Finding the Principal, given $75 interest at 7.2%...

S.

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If a person earns $75 interest in an account paying 7.2% interest. Find the principal at the beginning of 383 days and the amount in the account at the end of 383 days. Actually, I know how to calculate the principal at the beginning of 383 days. Figuring out the problem at the end of the 383 days is what I need. Thanks.
 

Denis

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Very unclear...
looks like 75 / (.072/365*382) = 995.31 = beginning balance.

If not, CLARIFY your question.
 

tkhunny

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Interest compounding method?
Interest crediting method?

One must specify the whole problem.
 

S.

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tkhunny said:
Interest compounding method?
Interest crediting method?

One must specify the whole problem.
The whole problem states, "In 383 days, Troy McLain earned $75 interest in an account paying 7.2% interest. Find (a) the principal at the beginning of the 383 days and (b) the amount in the account at the end of 383 days."
 

TchrWill

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S. said:
If a person earns $75 interest in an account paying 7.2% interest. Find the principal at the beginning of 383 days and the amount in the account at the end of 383 days. Actually, I know how to calculate the principal at the beginning of 383 days. Figuring out the problem at the end of the 383 days is what I need. Thanks
Assuming you are dealing with compound interest:

S = P(1 + i)^n
S = the total sum
P = the investing principal
i = the periodic interest in decimal form
n = the number of interest bearing periods

Compounded yearly, 1 + i = 1.072 and n = 383/365 = 1.04931
S - P = P(1 + 1.072^1.04931 - P = P[(1.072)^1.04931 - 1]
Therefore, P = 75/[(1.072)^1.04931 - 1] = $991.00

Compoundiong monthly, (1 + i = 1.006 and n = 12.6) the same process yields P = $958.00

Compounding dailly, (1 + i = 1.00019726 and n = 383) yields P = $955.78

The sums at the end of 383 days derive from the same formula.

Compounded monthly, for instance, S = 958(1.006^12.6 = $1033
The interest gained is $1033 - $958 = $75.00

I'll let you compute the other 2.

If you are dealing with simple interest, .072 per year, then your starting principal would be derived from S - P = 75 = .072(383/365)P making P = $992.71.
 

tkhunny

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S. said:
The whole problem states
This probably is not correct. There must be more information. One possible chunk of information not given in the problem statement is that you are working in a section entitled "Simple Interest". That would help clarify the problem.
 

Denis

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Using 1 year = 360 days and simple interest:
75 / (.072 / 360 * 383) = 979.11 = opening balance

That amount will earn interest of $75, so balance at end will simply be:
979.11 + 75.00 = 1054.11 ; YES, it is that simple !
 
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