Question 1058562: How long will it take for $1300 to grow to $2300 at an interest rate of 6.4% if the interest is compounded quarterly? Round the number of years to the nearest hundredth.
Select one:
a. 8.99
b. 35.94
c. 27.86
d. 9.20
Answer by solve_for_x(190)   (Show Source):
You can put this solution on YOUR website! The formula for compound interest is:
FV = PV(1 + r/n)^(nt)
where FV is the future value, PV is the present value, r is the annual interest
rate, n is the number of periods per year, and t is the number of years.
For this problem, FV = 2300, PV = 1300, r = 0.064, and n = 4.
Substituting those values into the equation gives:
2300 = 1300(1 + 0.064/4)^(4t)
2300 = 1300(1.016)^(4t)
(1.016)^(4t) = 2300/1300
Taking the natural logarithm of both sides then gives:
4t * ln(1.016) = ln(2300/1300)
t = ln(2300/1300) / 4*ln(1.016)
t = 8.99 years
Check:
1300(1.016)^(4*8.99) = 1300(1.7697) = 2300.60
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