Question

Finding Present Value In Exercise,complete the table to determine the amount of money P that should be invested at rate r to produce a final balance of $100,000 in t years.See Example 5.
t 1 10 20 30 40 50
p
r = 4%,compounded monthly

Answer 1

Answer:

Step-by-step explanation:

The principal was compounded monthly. This means that it was compounded 12 times in a year. So

n = 12

The rate at which the principal was compounded is 4%. So

r = 4/100 = 0.04

The formula for compound interest is

A = P(1+r/n)^nt

A = total amount in the account at the end of t years. The total amount is given as $100000.

1) When t is 1,

100000 = P(1+0.04/12)^12×1

100000 = P(1+0.0033)^12

100000 = P(1.0033)^12

P = 100000/1.04

P = $96154

2) When t is 10

100000 = P(1+0.04/12)^12×10

100000 = P(1+0.0033)^120

100000 = P(1.0033)^120

P = 100000/1.485

P = $67340

3) When t is 20

100000 = P(1+0.04/12)^12×20

100000 = P(1+0.0033)^240

100000 = P(1.0033)^240

P = 100000/2.2

P = $45455

4) When t is 30

100000 = P(1+0.04/12)^12 × 30

100000 = P(1+0.0033)^360

100000 = P(1.0033)^360

P = 100000/3.274

P = $30544

5) When t is 40

100000 = P(1+0.04/12)^12 × 40

100000 = P(1+0.0033)^480

100000 = P(1.0033)^480

P = 100000/4.862

P = $20568

6)When t is 50

100000 = P(1+0.04/12)^12 × 50

100000 = P(1+0.0033)^600

100000 = P(1.0033)^600

P = 100000/7.22

P = $13850