At what rate will the sum of 1200 amount to 2348.32 in 2yrs? if compounded quarterly

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Answer 1 · 2018-05-11T21:55:38

#color(blue)(35.018%)#

The formula for compound interest is given by:

#FV=PV(1+r/n)^(nt)#

Where:

#FV= "future value"#.

#PV="present value"#

#r="interest rate given as a decimal"#

#n="compounding period"#

#t="time in years"#.

From given information, we have:

#t=2#

#n="quarterly"=4#

#PV=1200#

#FV=2348.32#

We are looking to find interest rate #r#:

#1200(1+r/4)^8=2348.32#

#(1+r/4)^8=2348.32/1200#

#(4+r)^8/4^8=2348.32/1200#

#(4+r)^8=4^8(2348.32/1200)#

#(4+r)^8=128249.5829#

#r=root(8)(128249.5829)-4=0.350177674#

This is in decimal form, so:

#r=35.018%#