Lincoln invested $930 in an account paying an interest rate of 5.6% compounded daily. Assuming no deposits or withdrawals are ma
de, how long would it take, to the nearest tenth of a year, for the value of the account to reach $2,320?
1 answer:
Answer:
16.3 years
Step-by-step explanation:
(see attached for reference on compounded interest)
recall that the formula for compound interest is
A = P [1 + (r/n) ]^(nt),
where
A = final amount = given as $2,320
P = principal amount = given as $930
r = rate = given as 5.6% = 0.056
n = number of times compounded per year = 365 since compounded daily
t = time taken in years (we are asked to find this)
Simply substitue the known values above into the equation
A = P [1 + (r/n) ]^(nt)
2320 = 930 [1 + (0.056/365) ]^(365t)
2320 = 930 [1.000153425]^(365t)
2320 / 930 = [1.000153425]^(365t) (taking log of both sides)
log (2320/930) = log { [1.000153425]^(365t) }
log (2320/930) = 365t log (1.000153425)
365t = log (2320/930) / log(1.000153425)
365t = 5958.6639
t = 5958.6639/365
t = 16.325 years
t = 16.3 years (to nearest tenth of a year)
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