You currently have $7,400 (Present Value) in an account that has an interest rate of 7.5% per year compounded semi-annually (2 times per year). You want to withdraw all your money when it reaches $14,060 (Future Value). In how many years will you be able to withdraw all your money?
Given,
Present value = $7400
Interest rate = 7.5% or 0.075
Future value = $14060
Solution :-
Semi annual interest rate (r) = 0.075/2 = 0.0375
Let semi annual periods be 'n'
Future value = Present value x (1 + r)n
$14060 = $7400 x (1 + 0.0375)n
$14060/$7400 = (1.0375)n
1.9 = (1.0375)n
Taking 'Log' both sides,
Log(1.9) = Log(1.0375)n
Log(1.9) = n.Log(1.0375)
0.64185388617 = n.(0.0368139731)
0.64185388617/0.0368139731 = n
17.4350615302 = n
Now,
Number of years = 17.4350615302/2 = 8.72 years
So, in 8.72 years you will be able to withdraw all your money.
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