An account now contains $10,118 and has been accumulating interest at 8% annual interest, compounded continuously, for 6 years. Find the initial deposit. Round your answer to the nearest cent.
A) $16,351.44
B) $9,340.09
C) $6,260.85
D) $6,376.06

Question

Quizplus · Accepted Answer

We can use the formula for continuous compounding:

A = Pe^(rt)

where:
A = final amount = $10,118
P = initial deposit (what we're solving for)
r = annual interest rate = 8% = 0.08
t = time in years = 6

Plugging in the values, we get:

$10,118 = Pe^(0.08*6)
$10,118 = Pe^0.48
ln($10,118) = ln(P) + 0.48
ln(P) = ln($10,118) - 0.48
P = e^(ln($10,118) - 0.48)
P = $6,260.85

So the initial deposit was $6,260.85, which is closest to choice C.

An Account Now Contains $10,118 and Has Been Accumulating Interest