# 12 Simple Interest

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```					           HOMEWORK 10. SELECTED SOLUTIONS

Exercise 10.2. Determine the simple interest (1 year = 12 months = 360
days). By default (unless otherwise noted), the rate is an annual rate.

a) p = \$450, r = 5.5%, t = 2 years;

b) p = \$41864, r = 0.0375% per day, t = 1 year;

c) p = \$365.45, r = 11.5%, t = 8 months.

Solution. a)

i = 450 × 0.055 × 2 = 49.50 Dollars.

b). In this case, we measure time in days: t = 360 days.
0.0375
i = 41864 ×          × 360 = 5651.64 Dollars.
100

8    2
c). In this case, t = 12 = 3 years.

11.5 2
i = 365.45 ×       × = 28.10 Dollars.
100  3
Exercise 10.3. Use the simple interest formula to determine the missing
value (1 year = 12 months = 360 days):

a) p =?, r = 3%, t = 90 days; i = \$600;

b) p = \$800, r = 6%, t =?, i = \$64.00;

c) p = \$1650.00, r =?, t = 6.5 years, i = \$343.20.

Solution. a)
90
600 = p × 0.03 ×            600 = p × 0.0075      80000 = p
360

Principal is 80 thousands dollars.

b)
16
64 = 800 × 0.06 × t         64 = 48t        =t.
12
16
Time is 12 years or 16 months.

c)

343.20 = 1650.00 × r × 6.5       343.20 = 10725r      0.032 = r .

Rate is r = 0.032 = 3.2%.

2
Exercise 10.4. The Sweet Tooth Restaurant borrowed °3000 on a note
dated May 15 with simple interest of 11%. The maturity date of the loan is
September 1. The restaurant made partial payments of °875 on June 15 and
°940 on August 1. Find the amount due on the maturity date of the loan.

According to the Table from the book, May 15 is the Day 135, June 15 is
Day 166, August 1 is Day 213, and September 1 is Day 244.

First, consider the time period from May 15 to to June 15. The number
of days between these two dates is 31. Therefore, the interest is
31
3000 × 0.11 ×      = 28.42 dollars.
360
When the restaurant pays 875 dollars, 28.42 dollars is used to pay the interest,
and 875 - 28.42 = 846.58 goes to reduce the principal. So, the June 15th
principal is 3000 - 846.58 = 2153.42 dollars.

Second, consider the time period between June 15 and August 1. The
number of days is 213 - 166 = 47. Therefore, the interest is
47
2153.42 × 0.11 ×       = 30.93 dollars.
360
When the restaurant pays 940 dollars, 30.93 dollars is used to pay the interest,
and 940 - 30.93 = 909.07 goes to reduce the principal. So, the August 1st
principal is 2153.42 - 909.07 = 1244.35 dollars.

Finally, there are 31 days between August 1st and September 1. The
interest is
31
1244.35 × 0.11 ×     = 11.79 dollars.
360

So, the amount due is the latest principal plus the latest interest, or

1244.35 + 11.79 = 1256.14 dollars.

3
Exercise 10.5. The U.S. government borrows money by selling Treasury
bills. Treasure bills are discounted notes. On August 31, 2003, Trinity Lopez
purchased a 364-day, °6000 Treasury bill at 4.4% discount.

a) What is the date of maturity of the Treasure bill (2004 is a leap year)?

b) How much did Trinity actually pay for the Treasury bill?

c) How much interest did the U.S. government pay Trinity on the day of
maturity?

d) What is the actual rate of interest of the Treasury bill?

Solution. Consider the time period between August 31, 2003, and Au-
gust 31, 2004. Since we have the leap year 2004, and February 29, 2004 is
between those two dates, the number of days in this time period is equal to
366. Thus, the maturity date is 366-364 = 2 days before August 31, 2004,
i.e. it is August 29, 2004.

Trinity paid °6,000 dollars with 4.4% discount. The discount amount
(the interest) is
4.4
6000 ×       = 264 dollars.
100

Trinity actually paid

6000 − 264 = 5736 dollars.

The actual rate r is calculated from the Simple Interest Formula:
264
5736 × r × 1 = 264          r =        × 100% = 4.60% .
5736

4
Exercise 10.8. Use the Compound Interest formula to compute: 1) the
total amount; 2) the interest earned on each investment; 3) the Annual
Percentage Yield; if the following investment is made:

a) \$2000 for 3 years at 2.00% compounded semiannually;

b) \$2000 for 3 years at 2.00% compounded quarterly;

c) \$2000 for 3 years at 2.00% compounded monthly;

d) \$2000 for 3 years at 2.00% compounded daily.

Solution. a). The total amount is
(3·2)
0.02
A = 2000 × 1 +                    = 2000 × 1.016 = 2123.04 .
2

The interest is

i = A − p = 2123.04 − 2000.00 = 123.04 .

The APY is computed from the simple interest formula

2000 × rAP Y × 3 = 123.04
6000 × rAP Y   = 123.04
rAP Y   = 123.04 × 100% = 2.05% .
6000

5
b) The total amount is
(3·4)
0.02
A = 2000 × 1 +                      = 2000 × 1.00512 = 2123.36 .
4

The interest is

i = A − p = 2123.36 − 2000.00 = 123.36 .

The APY is computed from the simple interest formula

2000 × rAP Y × 3 = 123.36
6000 × rAP Y    = 123.36
rAP Y    = 123.36 × 100% = 2.06% .
6000
c) The total amount is

(3·12)                      36
0.02                             12.02
A = 2000 × 1 +                       = 2000 ×                = 2123.58 .
12                               12

The interest is

i = A − p = 2123.58 − 2000.00 = 123.58 .

The APY is computed from the simple interest formula

2000 × rAP Y × 3 = 123.58
6000 × rAP Y    = 123.58
rAP Y    = 123.58 × 100% = 2.06% .
6000

6
d) The total amount is

(3·360)                         1080
0.02                               360.02
A = 2000 × 1 +                       = 2000 ×                     = 2123.67 .
360                                 360

The interest is

i = A − p = 2123.67 − 2000.00 = 123.67 .

The APY is computed from the simple interest formula

2000 × rAP Y × 3 = 123.67
6000 × rAP Y    = 123.67
rAP Y    = 123.67 × 100% = 2.06% .
6000

Exercise 10.9. Marcella Laddon wins third prize in Clearinghouse Sweep-
stakes and receives a check for \$250000. After spending \$10000 on a vacation
she decides to invest the rest in a money market account that pays 1.5% in-
terest compounded monthly. How much money will be in her account after
10 years?

Solution. The principal is

p = 250000 − 10000 = 240000 dollars.

Using the Compound Interest Formula, we get

(12·10)                            120
0.015                                  12.015
A = 240000 × 1 +                         = 240000 ×                     = 278814.10
12                                      12

in 10 years, she will have 278814.10 dollars (her interest is about 39 thousands
dollars).

7

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