SAINT COLUMBAN COLLEGE
Pagadian City
ND
2 Semester S.Y 2023 – 2024
MATH 509
FOUNDATION OF MODERN MATHEMATICS
Masterand: Diosa Mae M. Ybañez
Date: March 09, 2024
Professor: Rainerio M. Salomes, EdD
Assignment 4: Simple and Compound Interest
Solve the following problems:
1. How much will be the future worth of money after 12 months if the sum of P35,000 is invested today at a simple
interest rate of 3% per month.
𝐹𝑉 = 𝑃(1 + 𝑟𝑡) = 35,000(1 + 0.03 × 12) = 35,000(1 + 0.36) = 35,000 × 1.36
= 𝟒𝟕, 𝟔𝟎𝟎. 𝟎𝟎
Therefore, the future worth of the money after 12 months will be 47,600 pesos.
2. A man expects to receive P125,000 in eight years. How much is that money worth now considering an interest rate
of 12% compounded quarterly?
𝑃𝑉 =
𝑃𝑉 =
𝐹𝑉
𝑟 𝑛𝑡
(1 + 𝑛)
125000
0.12 4×8
(1 + 4 )
𝑃𝑉 =
125000
(1 + 0.03)32
𝑃𝑉 =
125000
2.5751
𝑷𝑽 ≈ 𝟒𝟖, 𝟓𝟒𝟏. 𝟖𝟎
So, the money is worth approximately P48, 541.80 now, considering an interest rate of 12% compounded
quarterly.
3.
How long will it take the money to triple itself if invested at 9.5% compounded semi-annually?
𝑟 𝑛𝑡
𝐹𝑉 = 𝑃𝑉 (1 + )
𝑛
0.095 2𝑡
3𝑃𝑉 = 𝑃𝑉 (1 +
)
2
3 = (1 + 0.0475)2𝑡
𝐼𝑛(3) = 2𝑡 𝐼𝑛(1.0475)
𝑡=
𝐼𝑛(3)
2 𝐼𝑛(1.0475)
𝑡≈
1.098612
0.092813
𝒕 ≈ 𝟏𝟏. 𝟖𝟒
So, it will take approximately 11.84 years for the money to triple itself when invested at 9.5% compounded
semi-annually.
4.
Which terms offer the best investment for 1 year?
a. 10% simple interest
b. 9.6% compounded monthly
c. 10% compounded daily
a.
𝐹𝑉 = 𝑃𝑉(1 + 𝑟𝑡)
𝐹𝑉 = 𝑃𝑉(1 + 0.10 × 1)
𝐹𝑉 = 𝑃𝑉 × 1.10
b.
𝑟 𝑛𝑡
𝐹𝑉 = 𝑃𝑉 (1 + 𝑛)
0.096 12×1
𝐹𝑉 = 𝑃𝑉 (1 + 12 )
𝐹𝑉 = 𝑃𝑉(1 + 0.008)12
𝐹𝑉 ≈ 𝑃𝑉 × 1.104712
c.
𝑟 𝑛𝑡
𝐹𝑉 = 𝑃𝑉 (1 + 𝑛)
0.10 365
𝐹𝑉 = 𝑃𝑉 (1 +
)
365
𝐹𝑉 ≈ 𝑃𝑉 × 1.105170
The best investment is c. 10 % compounded daily.
5. Find the amount due on P200,000 in 4 years and 3 months at
a. 4 ¼ % compounded semi-annually
b. 5 ½ % compounded quarterly
c. 6 % compounded annually
d. 7 % simple interest
𝑟 𝑛𝑡
a. 𝐴 = 𝑃 (1 + 𝑛)
0.0425 2×4.25
)
2
𝐴 = 200, 000(1 + 0.02125)8.5
𝐴 = 200, 000(1.02125)8.5
𝐴 = 200, 000(1.195700)
𝑨 = 𝟐𝟑𝟗, 𝟏𝟒𝟎
𝐴 = 200, 000 (1 +
So, the amount due on P200, 000 in 4 years and 3 months at 4 ¼ % compounded semi-annually is
P239, 140.
𝑟 𝑛𝑡
b. 𝐴 = 𝑃 (1 + 𝑛)
0.055 4×4.25
𝐴 = 200, 000 (1 +
)
4
𝐴 = 200, 000(1 + 0.01375)17
𝐴 = 200, 000(1.01375)17
𝐴 = 200, 000(1.261318)
𝑨 ≈ 𝟐𝟓𝟐, 𝟐𝟔𝟑. 𝟔𝟎
So, the amount due on P200, 000 in 4 years and 3 months at 5 ½ % compounded quarterly is approximately
P252, 263.60.
c. 𝐴 = 𝑃(1 + 𝑟)𝑡
𝐴 = 200,000(1 + 0.06)4.25
𝐴 = 200,000(1.06)4.25
𝐴 = 200,000(1.281002)
𝑨 ≈ 𝟐𝟓𝟔, 𝟐𝟎𝟎. 𝟒𝟎
So, the amount due on P200,000 in 4 years and 3 months at 6% compounded annually is approximately
P256, 200.40
d. 𝐴 = 𝑃(1 + 𝑟𝑡)
𝐴 = 200,000(1 + 0.07 × 4.25)
𝐴 = 200,000(1.2975)
𝑨 = 𝟐𝟓𝟗, 𝟓𝟎𝟎
So, the amount due on P200, 000 in 4 years and 3 months at 7% simple interest is P259,500.