AnimeAngel29idn
Answered

Sumali sa IDNStudy.com at makakuha ng mga sagot ng eksperto. Ang aming platform ng tanong at sagot ay idinisenyo upang magbigay ng mabilis at eksaktong sagot sa lahat ng iyong mga tanong.

If an amount of money P in pesos is invested at r percent compounded annually, it will grow to an amount A=P(1+r)² in two years. Suppose Mrs. Madrigal wants her money amounting to Php 200 000 to grow to Php 228 980 in two years. At what rate must she invest her money?


I need the process of the solution.. please help me.. thanks

Sagot :

Mlcparra16idn
We have A=228,980 and P=200,000

A = P(1+r)²
228,980 = 200,000(1+r)²
228,980 = 200,000(r²+2r+1)
228,980 = 200,000r² + 400,000r + 200,000
0 = 200,000r² + 400,000r - 28,980
0 = 10,000 r² + 20,000r - 1,449

We then use the quadratic formula:
r = -20,000 ± √(20,000²+4·10,000·1449) = -20,000 ± √457960000 
                     2(10,000)                                    20,000)
= -20,000 ± 21,400  = -100 ± 107 = -207/100 or 7/100
          20,000                 100

We take the positive rate which is 7%. So r=7%.
Hmm, now I can post the solution here I have posted in the comment section ten hours ago (check above).

A= 228, 980
P= 200, 000
r = rate 

228,980 = 200,000 (1 + r)²
228,980 = 200 000 (1 + 2r + r²)
228,980 = 200 000 + 400 000 r + 200 000r²
200 000 r² + 400 000 r + 200 000 - 228 980 = 0
2000 000 r² + 400 000 r -28 980 = 0

Factor or use the quadratic formula:

( x - 7/100 ) (x + 207/100) = 0

x = 7/100    or x = -207/100

Choose the positive root, x-value: 7/100

7/100 = 0.07 = 7 percent

The rate is 7 %