Chapter 12 Sequences; Induction; the Binomial Theorem

Chapter 12: Sequences; Induction; the Binomial Theorem
(c) Enter the recursive formula in Y= and
create the table:
b.
⎛ 0.065 ⎞
⎜1 + ⎟(120,000) −758.48
= $119,891.52
⎝ 12 ⎠
c. Enter the recursive formula in Y= and create
the table:
(d) Scroll through the table:
d. Scroll through the table:
After 37 payments have been made, the
balance is below $140,000. The
balance is $139,894.
(e) Scroll through the table:
After 129 payments have been made, the
balance is below $100,000. The balance is
about $99,824.
e. Scroll through the table:
The loan will be paid off at the end of
279 months or 23 years and 3 months.
Total amount paid = (278)($999.33) +
353.69(1.005) = $278,169.20
(f) The total interest expense is the
difference of the total of the payments
and the original loan:
278,169.20 − 150,000 = $128,169.20
h. Yes, if they can afford the additional
monthly payment. They would save
$44,586.07 in interest payments by paying
the loan off sooner.
90. a. Since the interest rate is 6.5% per annum
compounded at a rate of (6.5/12)% each
month. Defining a recursive sequence, we
have:
a0
= 120,000,
⎛ 0.065 ⎞
an
= ⎜1+ ⎟an
− 1 −758.48
⎝ 12 ⎠
The loan will be paid in the 360th month i.e.
after 30 years.
Total amount paid = (359)(758.48) +
756.19(1+0.065/12) = $273,054.60.
f. The total interest expense is the difference
of the total of the payments and the original
loan: 273,054.60 − 120,000 = $153,054.60
g. (a) Since the interest rate is 6.5% per
annum compounded monthly, this is
equivalent to a rate of (6.5/12)% each
month. Defining a recursive sequence,
we have:
a0
= 120,000,
⎛ 0.065 ⎞
an
= ⎜1+ ⎟an
− 1 −858.48
⎝ 12 ⎠
1242
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