Google has just purchased your website that reviews gps systems. you made a profit of $65,000. you would like to invest the $65,000 into an account that pays you an annual compounded interest rate of 5.5%. you want to make annual withdrawals over the next 10 years such that by the end of this 10 year period, the amount remaining in the account will be zero dollars. determine, from the given information, the amount of the annual withdrawals. round your answer to the nearest cent. a. $6,500 c. $7,251.31 b. $7,023.45 d. $8,623.40

In this type of problem, it is important to understand

1. the first withdrawal is at the beginning or end of the first period.

2. the compounding period.

This question indicates 10 annual withdrawals the last one of which leaves zero after the tenth year, so first withdrawal is at the end of the first year.

Also, the interest rate says "an annual compounded interest rate of 5.5%" which may not have specified the compounding period. However, if it said "an annualLY compounded interest rate of 5.5%" would make it clear that the compounding period is annual. I assume the latter interpretation.

The problem is basically one of a mortgage payment (in reverse) or annuity payments. The present value is compounded over 10 years, with yearly withdrawals (or payments for a mortgage).

The equation required to calculate the equal annual withdrawal is as follows

where

A=annual withdrawal, to be found

P=present value = 65000

i=interest per compounding period (year) = 0.055

n=number of compounding periods = 10

Substituting values,

A=P(i(1+i)^n)/((1+i)^n-1)

=65000(0.055(1.055^10)/(1.055^10-1))

take out your calculator to get

=8623.40 (to the nearest cent)

a - base

b - exponent

so,

let's first notice, the center of the hyperbola is at the origin, since the focus points are equidistantly 3 units away from the origin, that also means that the distance "c" from the center to either focus is 3.

it should also be notable that, the traverse axis for this hyperbola is vertical, or namely over the y-axis and therefore, the positive fraction will be the one with y-variable.

the traverse "a" component or distance from the center to either vertex is not 2, is more than 2, so we can safely put it at √5 ≈ 2.24.