Solving for Unknown Time

Problem 14.1
The present value of a payment of $5,000 to be made in $t$ years is equal to the present value of a payment of $7,100 to be made in $2t$ years. If $i = 7.5\%$ find $t4.

Solution.

$$5,000(1+0.075)^{-t} = 7,100(1+0.075)^{-2t} \\ \implies 5,000 = 7,100(1 + 0.075)^{-t} \\ \implies t = 4.8486$$