Question

If an IRA is a variable-rate investment for 25 years at rate r percent per year, compounded monthly, then the future value S that accumulates from an initial investment of $1000 is s = 100011 + 0.01r]300 12 What is the rate of change of S with respect to r and what does it tell us if the interest rate is as follows? (Round your answers to two decimal places.) (a) 6% If we were to increase the rate by 1%, the future value of the investment would increase by about $ (b) 12% If we were to increase the rate by 1%, the future value of the investment would increase by about $

Answer 1

0.010. s-100011+뾔3000 s-1000| 1 + 0.011300

When r=6%

S=1000(1+0.01*6/12)^300=1000*(1+0.06/12)^300=1000*(1+0.005)^300=1000*4.4749=4474.97

At r+1=7%

S=1000(1+0.01*7/12)^300=1000*(1+0.07/12)^300=1000*(1+0.005833)^300=1000*5.7254=5725.4

Increase in Future value of S=5725.4-4474.97=$1260.448

When r=12%

Future value

S=1000(1+0.01*12/12)^300=1000*(1+0.1)^300=1000*(1.01)^300=1000*19.78847=19788.47

At r+1=13%

S=1000(1+0.01*13/12)^300=1000*(1+0.01083)^300=1000*(1.01083)^300=1000*25.34349=25342.4

Increase in future value of =25342.4-19788.47=$5555.025