Let $ 1 is invested today ,so in 13 years Future value =$ 4
Number of quarters = 13 *4 = 52 quarters [4quarters in a year comprising of 3 months each]
using the formula ,
Future value =present value (1+i)^n
where i = quarterly interest rate
n=number of quarters
Now,putting the valurs in equation
4 =1 (1+i)^52
Multiplying both sides by ^1/52
(4)^1/52 = (1+i)^52*1/52
(4)^1/52 = (1+i)
(4)^.019231 = 1+i [Find the value of (4)^.019231 using financial calculator )
1.027018 - 1 = =i
i = .027018 or 2.7018 %
quarterly interest rate = 2.70%
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