Mathematics, 20.02.2020 02:15 dbrwnn
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%
Answers: 2
![S=2000\cdot\left[1+\frac{0.01 \cdot r}{12}\right]^{300}](/tpl/images/0516/6000/61097.png)
![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](/tpl/images/0516/6000/0381f.png)
![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](/tpl/images/0516/6000/d8826.png)
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