As part of your retirement, you wish to generate $2,000 monthly payments for a 15-year period. The annual interest rate is 5%. What minimum amount is necessary to fund these payments?

$962.0

Step-by-step explanation:

The formula for amount is ;

where

A= amount at the end of the period= $2000

P=minimum amount necessary to fund the payments

r= annual interest rate = 5% = 0.05

n= number of compounding per year , 1

t= time period = 15 years

Applying the values to the formula as;

answer: 21$

step-by-step explanation:

$42 / $14 = 3   (ratio 3: 1)

$7 x 3 = $21

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt