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 $2000 is S = 2000 [1 + 0.01r /12]300
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%

b) 12%

Answer 1

Answer:

a) S=8667.30.

b) S=39576.93.

Step-by-step explanation:

We know that the future value S that accumulates from an initial investment of $2000 is

$S=2000\cdot\left[1+\frac{0.01 \cdot r}{12}\right]^{300}$

a) If r=6%, we get:

$S=2000\cdot\left[1+\frac{0.01 \cdot r}{12}\right]^{300}\\\\S=2000\cdot\left[1+\frac{0.01 \cdot 6}{12}\right]^{300}\\\\S=2000\cdot (1.0049)^{300}\\\\S=8667.30$

Therefore, we get that S=8667.30.

b) If r=12%, we get:

$S=2000\cdot\left[1+\frac{0.01 \cdot r}{12}\right]^{300}\\\\S=2000\cdot\left[1+\frac{0.01 \cdot 12}{12}\right]^{300}\\\\S=2000\cdot (1.01)^{300}\\\\S=39576.93$

Therefore, we get that S=39576.93.

If the interest rate is higher, we also get S higher.