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27 September, 08:02

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

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  1. 27 September, 08:22
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    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
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