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.