Alexei wants to save for a graduation trip. He deposits $750 every 6 months into an account that earns 6.7% per year compounded semi annually (twice a year).

Question

a) What is the amount in his account after 3 years? (use formula)

b) How much interest did he earn?

Answer 1

Po = PV = Present Value = $750

$6431.32 in 3 years at 6.7% annual interest adding $750 every 1/2 year, compounded semiannually

FV = Future Value = Principal plus interest

time t=0 Value = FV = PV = $750= the initial principal

time t = 1/2 year, FV = 750 +750 + 750(.067) = 1500 +50.25 = 1550.25

time t = 1 year FV = 1550.25 + 750 + 1550.25(.067) = 2300.25 + 103.87= 2404.12

time t = 1.5 years FV = 2404.12 + 750 + 2404.12(.067) = 3154.12 + 161.08=3315.20

time t = 2 years FV= 3315.20 +750 + 3315.20(.067) = 4065.20 + 222.12= 4287.32

time t = 2.5 years FV= 4287.32 + 750 + 4287.32(.067) = 5037.32 + 287.25= 5324.57

time t = 3 years FV = 5324.57 +750 + 5324.57(.067) = 6074.57 +356.75= $6431.32

t= 0 $750

t=1/2 1500

t=1 2250

t =1.5 3000

t= 2 3750

t = 2.5 4500

t = 3 $5250

= 750x7 = 5250, 6 times you added 750, plus the original 750 = 7 times 750

interest = 6431.32 - 5250 = $1,181.32

= the semiannual compounded interest at 6.7% APR

or

750(1.067)^(2(3)) = 1106.75 which is "close" to 1181.32 calculated above