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

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