Compound Interest

QUESTION

A financial institution is advertising a new 3-year investment certificate. The interest rate is 7.5% compounded quarterly the first year, 6.5% compounded monthly the second year, and 6% compounded daily the third year. What rate of interest compounded semi-annually for 3 years would a competing ins
tLet the amount be invested $1.00 The interest rate is 7.5% At the end of the first year interest = (1 r) t r = 7.5×3/12×1/100 =(1 7.5×3/12×1/100 )4 =(1 0.01875)4 =(1.01875)4 =1.01875^4 =1.077135866 At the end of the first year amount =$1.00×1.077135866 =1.077135866 In the second year interest rate =(1 r)t =(1 6.5/100 )12 =1.065 ^12=2.129096 =1.077135866×2.129096 At the end of the second year amount=2.29332566 In the third year interest =(1 r)t r=6/100×1/360 r =0.000166 =(1

0166)360 =1.061576471 At the end of the third year amount=1.061576471×2.29332566=2.434540561 Rate of interest compounded semi annually of 3 years=6 (1 r)6=2.44 The future value factor of 2.44 corresponding to six periods in future value table. We will see that a futuru value factor of 2.44 corresponds to the 16% column o

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