GABANO, JAYSON
TCPE 2-1
TCCB 421 - ENGINEERING ECONOMICS
Final Homework 01
Questions:
1.
What is the current value of a $50 payment to be made at the beginning of each
year, for three years if the prevailing rate of interest is 7% compounded annually?
Given:
𝐴 = 50
𝑖 = 0. 07
Solution:
−𝑛
𝑃 = 𝐴[
1−(1+𝑖)
𝑖
](1 + 𝑖)
−3
𝑃 = 50[ 1−(1+(0.07))
0.07
](1 + 0. 07)
−3
𝑃 = 50[ 1−(1.07)
0.07
𝑃 = 140. 40
](1. 07)
𝑛= 3
2.
What is the accumulated value of a $25 payment to be made at the beginning of
each of the next three years if the prevailing rate of interest is 9% compounded annually?
Given:
𝐴 = 25
𝑖 = 0. 09
𝑛= 3
Solution
𝑛
𝐹 = 𝐴[ (1+𝑖)𝑖 −1 ](1 + 𝑖)
3
𝐹 = 25[
(1+0.09) −1
0.09
](1 + 0. 09)
3
𝐹 = 25[
(1.09) −1
0.09
](1. 09)
𝐹 = 89. 33
3.
How much should Mr. Sy invest on a bank that offers 10% interest so that he
would earn Php1,000 each year in perpetuity?
Given:
𝑖 = 0. 1
Solution:
𝑃 =
𝐴
𝑖
𝑃 =
1000
0.1
𝑃 = 10,000
𝐴 = 1000
𝑛 = 𝑝𝑒𝑟𝑝𝑒𝑡𝑢𝑖𝑡𝑦
4.
Don Jose deposited Php5,000,000 on a bank that earns 10% compounded
annually. Five years later he died. His will states that his beneficiary is an orphanage
which will be receiving the money in perpetuity a year after he died. How much is the
yearly fund the orphanage will be receiving?
Given:
𝑃 = 5 000 000
𝑖 = 0. 1
𝑛 = 5, 𝑝𝑒𝑟𝑝𝑒𝑡𝑢𝑖𝑡𝑦
Solution:
𝐴 = 𝑖𝑃(1 + 𝑖)
𝑘
𝐴 = (0. 1)(5, 000, 000)(1 + 0. 1)
5
𝐴 = 805,255
If money is worth 8% compounded quarterly, compute the present value of the
perpetuity of Php1,000 payable quarterly.
Given:
𝑖 =
𝑟
=
0.08
𝑚
Solution:
𝑃 =
𝐴
𝑖
𝑃 =
1000
0.02
𝑃 = 50,000
4
= 0. 02
𝐴 = 1000