Paco decides to invest $600 into a bank account that gives him a 3.4% interest rate compounded quarterly. He wants to know how long it will take for him to save up to $1,000.

It would take 15 years

Step-by-step explanation:

The length of time it takes to reach $1,000 savings can be determined from the future value formula given below:

FV=PV * (1+r/4) ^n*4

FV is the target savings of $1,000

PV is the amount invested which is $600

r is the rate of interest of 3.4%

n is the unknown

1000=600 * (1+3.4%/4) ^4n

1000=600 * (1+0.0085) ^4n

1000=600 * (1.0085) ^4n

1000/600=1.0085^4n

1.666666667 = 1.0085^4n

take log of both sides

ln 1.666666667 = 4n ln 1.0085

4n=ln 1.666666667/ln 1.0085

4n=0.510825624 / 0.008464078

4n=60.35218768

n=60.35218768 / 4

n = 15.09