A financial institution is advertising a new 3-year investment certificate. The
ID: 2663759 • Letter: A
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 institution have to offer to match the interest produced by this investment certificate? Let the amount invested by $1.00. Also give the maturity value of the investment and equivalent future value compounded semi-annually.Explanation / Answer
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 = 7.5x3/12x1/100
=(1+7.5x3/12x1/100)4
=(1+0.01875)4
=(1.01875)4
=1.01875^4
=1.077135866
At the end of the first year amount =$1.00x1.077135866
=1.077135866
In the second year interest rate =(1+r)t
=(1+6.5/100)12
=1.065 ^12=2.129096
=1.077135866x2.129096
At the end of the second year amount=2.29332566
In the third year interest =(1+r)t
r=6/100x1/360
r =0.000166
=(1+0.000166)360
=1.061576471
At the end of the third year amount=1.061576471x2.29332566=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
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.