If 101 is given in base <em>b</em>, then in base 10 you have
For instance, if <em>b</em> = 2, then
101₂ = 2² + 1 = 5₁₀
If <em>b</em> = 3, then
101₃ = 3² + 1 = 9₁₀
If <em>b</em> = 4, then
101₄ = 4² + 1 = 17₁₀
The answer depends entirely on the base of the given number.
9514 1404 393
Answer:
a) $7715.10
b) $6022.02
c) 15263.10
Step-by-step explanation:
A calculator or spreadsheet can evaluate the formulas for you using the given parameters.
The compound interest formula is ...
A = P(1 +r/n)^(nt)
where P is the principal amount, r is the annual rate, n is the number of times interest is compounded per year, and t is the number of years.
The continuously compounded interest formula is ...
A = Pe^(rt) . . . . where P, r, t are defined as above
Often the function e^x is defined as the exp(x) function.
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A calculator or spreadsheet can perform rounding for you, but we elected not to confuse the issue with that step. The calculator results below are rounded in the answer list above.
For part (a), we have ignored the fact that 7 years will have an additional week, since there are 1 or 2 extra days (beyond 52 weeks) in each year. Taking that into account adds a penny to the account balance.
The extra day in a leap year affects the account balance in the 8th significant figure. Our balance has only 6 significant figures, so we do not need to be concerned with the effect of a possible leap year in the 3-year period of part (b).
