Refresher - MATHEMATICS Quiz 9
PROBLEM 1:
An engineer who is about to retire has accumulated P50,000 in a savings
account that pays 6% per year compounded annually. Suppose the
engineer wishes to withdraw a fixed sum of money at the end of each
year for 10 years. What is the amount that can be withdrawn?
Capital Recovery Factor: (A/P, 6%, 10) = 0.1359
Gredient Uniform Series: (A/G, 6%, 10) = 4.022
Uniform Series Compound Amount Factor: (F/A, 6%, 10) = 13.1808
Single Payment Compound Amount Factor: (F/P, 6%, 10) = 1.7908
Solution:
A ⎡⎣(1 + i)n - 1⎤⎦
P=
(1 + i)n i
A (1 + i)n i 0 1 2 3 n
=
P (1 + i)n - 1
A A A A
A
= 0.1359
P
P=50,000
A
= 0.1359
50,000
A = P6,795
, Refresher - MATHEMATICS Quiz 9
PROBLEM 2:
Given the vector A = 3i – 6j + 2k. Compute the angle which the vector makes with
the x-axis.
SOLUTION:
A = 3i - 6j + 2k
R = (3)2 + (- 6)2 + (2)2
R =7
3
Cos θx =
7
θx = 64.6˚
PROBLEM 1:
An engineer who is about to retire has accumulated P50,000 in a savings
account that pays 6% per year compounded annually. Suppose the
engineer wishes to withdraw a fixed sum of money at the end of each
year for 10 years. What is the amount that can be withdrawn?
Capital Recovery Factor: (A/P, 6%, 10) = 0.1359
Gredient Uniform Series: (A/G, 6%, 10) = 4.022
Uniform Series Compound Amount Factor: (F/A, 6%, 10) = 13.1808
Single Payment Compound Amount Factor: (F/P, 6%, 10) = 1.7908
Solution:
A ⎡⎣(1 + i)n - 1⎤⎦
P=
(1 + i)n i
A (1 + i)n i 0 1 2 3 n
=
P (1 + i)n - 1
A A A A
A
= 0.1359
P
P=50,000
A
= 0.1359
50,000
A = P6,795
, Refresher - MATHEMATICS Quiz 9
PROBLEM 2:
Given the vector A = 3i – 6j + 2k. Compute the angle which the vector makes with
the x-axis.
SOLUTION:
A = 3i - 6j + 2k
R = (3)2 + (- 6)2 + (2)2
R =7
3
Cos θx =
7
θx = 64.6˚
