Answer:
- B. $352.19
- B. $9,126.53
- D. $123,866.02
Step-by-step explanation:
First of all, the formulas need to be written correctly, and you need to understand what the variables mean. Usually, the variables have these meanings:
- A — the amount you're trying to find, often a payment or balance
- P — the principal amount invested or borrowed
- r — the interest rate, often annual, sometimes the rate for the interval
- n — the number of intervals in the year for purposes of interest compounding
- t — the number of years (or intervals)
Usually, an annual interest rate is quoted and compounding is annual (n=1), quarterly (n=4) or monthly (n=12). In some formulas, r is the monthly rate and n is the number of months (there is no "t" in such formulas).
When we say "written correctly", we mean that parentheses are needed around exponents and denominators. In the formulas you have here, necessary parentheses are missing or misplaced, so you cannot use these formulas directly in your calculator or spreadsheet. If you're copying formulas from a question where they're typeset, be aware of the grouping effect of fraction bars and superscripts and use parentheses accordingly.
In the first two problems, you're not given P directly. Rather, the principal invested is to be computed as 10% of the amount given as "earnings."
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1. P = $147; r = 0.035; n = 12; t = 25.
A = P(1 + r/n)^(nt) = 147·(1 + .035/12)^(12·25) ≈ 147·1.002916667^300
A ≈ 352.19 . . . . matches choice B
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2. P = $3600; r = 0.0625; n = 4; t = 15.
A = P(1 + r/n)^(nt) = 3600·(1 + .0625/4)^(4·15) ≈ 3600·1.01625^60
A ≈ 9126.53 . . . . matches choice B
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3. P = $208; r = 0.05/12; n = 300. Here, r is the monthly rate, n is the number of months. Please note the correction of the formula. The variable "S" refers to the Sum of payments and interest. This is effectively the sum of a geometric sequence, so the formula should look familiar on that basis.
S = P((1 +r)^n -1)/r = 208·((1.004166667^300 -1)/0.004166667
S ≈ 123,866.02 . . . . matches choice D
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