A. Use the appropriate formula to determine the periodic deposit. B. How much of the financial goal comes from deposits and how much comes from​ interest?
Periodic Deposit: $? at the end of each year
Rate: 7​% compounded annually
Time: 18 years
Financial Goal: ​$130,000

The periodic deposit is? $

A. Periodic deposit:

The goal is to make $130,000 by depositing a set amount every year.

This set amount is an annuity. The $130,000 is therefore the future value of the annuity after 18 years.

Future value of annuity = Annuity * Future value of annuity factor, 7%, 18 years

130,000 = Annuity * 33.9990

Annuity = 130,000 / 33.9990

= $3,823.64

B. Sources of the financial goal.

Money from deposits = Periodic deposit * no. of years

= 3,823.64 * 18

= $68,825.52

Money from interest:

= Financial goal - Money from deposits

= 130,000 - 68,825.52

= $61,174.48

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

in geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. by extension, a line and a plane, or two planes, in three-dimensional euclidean space that do not share a point are said to be parallel.