Page 78 - CalcBus_Flipbook

8-28 Compound Interest CH 8]

5. Tommy Rawl inherited $145,000 on the day he became 19 years old. Under the
specifications of the will, the money was placed in a trust fund that earned interest at 9%
compounded semiannually. What amount was in his fund on Rawl’s twenty-second
birthday?
Time in the fund: 22 - 19 = 3 yrs
n
S = (1 + r ) x P r = % / payments per year = 0.09 / 2 yr = 0.045
I = S - P n = time x payments per yr = 3 x 2 = 6
NOTE:
6
Have learners be S = (1 + 0.045) x $145,000 = $188,827.72
judiciously cautious
with the number of 6. Ten years ago, the original amount in an account was $8,500. The interest rate is 6% paid
times they push the semiannually. Calculate (a) the simple interest value of this account and the total value of
‘=‘ key button for the account (principal + interest). Calculate (b) the compounded interest value for the
exponent value. Too account and (c) the interest generated by compounding. Table 8.1.
many pushes yield Solution algorithm:
the wrong answer.
(a) Simple interest I = P x r x t
I = $8,500 x 0.06 x 10 = $5,100.00 interest
Value of Account: P + I = $8,500.00 + $5,100.00 = $13,600.00

(b) Compound interest
n
S = (1 + r ) x P r = % / payments per year = 0.6 / 2 = 0.03
I = S — P n = time x payments per yr = 10 x 2 = 20

S = (1 + 0.03) x $8,500 =
20
S = (1 + 0.03) 2 x 2 x 5 x $8,500 =
S = (1.03) 2 x 2 x 5 x $8,500 =
S = (1.03) 2 x 2 x 5 x $8,500 =
(b) S = 1.806111123464 x $8,500 = $15,351.9454 = $15,351.95 value of account rounded
$15,351.95 — $8,500 = $6,851.95 interest

(c) Using the compound interest table, Table 8.1 for 6% at 10 years compounded semiannually
and using the data in (b) above your factor number is found at C 3% n Row 20, and is
1.80611123

The equation for calculating the value of a fund or account is:
Factor x Principle = Value the amount in the account.
Therefore:
1.80611123 x $8,500 = $15,351.95 the value and amount in the account.
(c) $15,351.95 — $8,500 = $6,851.95 compound interest (earned over 10 years).

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