Maria Addai has been offered a future payment of $990 two years from now. If she can earn 8.2 percent compounded annually on her
2 answers:
Answer:
845.6306
Step-by-step explanation:
Firstly this is annuity based
Let, investment at beginning of year = <em>x</em>
Then value at year 1 end = x + (8.2% x)
Value at end of year 2 = (x + 0.082x) + (8.2% (x + 0.082x))
Now this value = $990
Therefore,
990 = (x + 0.082x) + ((x + 0.082x) 8.2%)
990 = x + 0.082x + 0.082x + 0.006724x = 1.170724x
x = 990/1.170724 = 845.6306
You might be interested in
Answer:
Step-by-step explanation:
You know how subtraction is the <em>opposite of addition </em>and division is the <em>opposite of multiplication</em>? A logarithm is the <em>opposite of an exponent</em>. You know how you can rewrite the equation 3 + 2 = 5 as 5 - 3 = 2, or the equation 3 × 2 = 6 as 6 ÷ 3 = 2? This is really useful when one of those numbers on the left is unknown. 3 + _ = 8 can be rewritten as 8 - 3 = _, 4 × _ = 12 can be rewritten as 12 ÷ 4 = _. We get all our knowns on one side and our unknown by itself on the other, and the rest is computation.
We know that ; as a logarithm, the <em>exponent</em> gets moved to its own side of the equation, and we write the equation like this:
, which you read as "the logarithm base 3 of 9 is 2." You could also read it as "the power you need to raise 3 to to get 9 is 2."
One historical quirk: because we use the decimal system, it's assumed that an expression like uses <em>base 10</em>, and you'd interpret it as "What power do I raise 10 to to get 1000?"
The expression means "the power you need to raise 10 to to get 100 is x," or, rearranging: "10 to the x is equal to 100," which in symbols is
.
(If we wanted to, we could also solve this: , so
)