Question

Suppose a man is 25 years old and would like to retire at age 60. ?Furthermore, he would like to have a retirement fund from which he can draw an income of ?$100,000 per yearlong dash?forever! How can he do? it? Assume a constant APR of 8?%.

He can have a retirement fund from which he can draw ?$100,000 per year by having ?$ ______ in his savings account when he retires.

Answer 1

Answer:

$1314.37

Step-by-step explanation:

We have to calculate final value i.e. balance to earn $100,000 annually from interest.

= $\frac{100,000}{0.08}$ = $1,250,000

Now, N = n × y  = 12 × 25 = 300

         I  = 8% =  APR = 0.08

        PV = 0  = PMT = 0

        FV = 1,250,000 = A

$A=\frac{PMT\times [(1+\frac{apr}{n})^{ny}-1]}{\frac{apr}{n}}$

$PMT=\frac{A\times (\frac{APR}{n})}{[(1+\frac{APR}{n})^{ny}-1]}$

$PMT=\frac{1,250,000\times (\frac{0.08}{12})}{[(1+\frac{0.08}{12})^{12\times 25}-1]}$

$PMT=\frac{1,250,000\times (0.006667)}{[(1+\frac{0.08}{12})^{12\times 25}-1]}$

$PMT=\frac{1,250,000\times (0.006667)}{[(1+0.006667)^{300}-1]}$

$PMT=\frac{\frac{25000}{3}}{[1.006667^{300}-1]}$

$PMT=\frac{\frac{25000}{3}}{6.340176}$

Monthly payment (PMT) = $1314.369409 ≈ $1314.37

$1314.37 is required monthly payment in order to $100,000 interest.