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

$1314.37

Explanation:

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

=
`(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=(PMT* [(1+(apr)/(n))^(ny)-1])/((apr)/(n))`

`PMT=(A* ((APR)/(n)))/([(1+(APR)/(n))^(ny)-1])`

`PMT=(1,250,000* ((0.08)/(12)))/([(1+(0.08)/(12))^(12* 25)-1])`

`PMT=(1,250,000* (0.006667))/([(1+(0.08)/(12))^(12* 25)-1])`

`PMT=(1,250,000* (0.006667))/([(1+0.006667)^(300)-1])`

`PMT=((25000)/(3))/([1.006667^(300)-1])`

`PMT=((25000)/(3))/(6.340176)`

Monthly payment (PMT) = $1314.369409 ≈ $1314.37

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