Unit2TimeandMoneyB - Lavarias - Lorenz Jay

 

1.

Today you invested ₱100,000 ₱100,000 into a fund that pays 25% int interest erest compounded ann annually. ually. Three yea years rs later, you borrow ₱50,000 from a bank at 20% annual interest and invest the the fund. Two years la ter y ou withdraw enough money from the bank to repay the bank loan and all all interest due on it. Thr ee yea rs after th e withdrawal, you start takin g ₱20 ₱20,00 ,000 0 per year o ut o f th e fund. Afte r 5 withdra withdrawal wals, s, you withdraw the balance balance in the fund. How much was withdrawn?

₱50,000

i = 0.20 annual interest

₱20,000 F13

F5

₱100,000

₱50,000

F7

i = 0.25 compounded annually

F12

 

 F   = 50000 ¿  F   =7 0 , 000

 F   =100 000 1+ 0.25   + 50 000 1 + 0.25   −72 000 1 + 0.25  F 7= 489532.47  6

486407.47 1 + 0.25 −20000 1+ 0.25

 1

 ( 1 +0.25 )5−1

= F 

 F 13 = ₱  1,650,321.47

2

.   A man wishes to provide a fund for his retirement such that from his 60th to 70th  birt hday s he will be ab able le to withd withdraw raw equ equal al su ms o off ₱ 18,000 18,0 00 f or h is year y early ly ex pen ses. He in vests ves ts equa e quall amounts for his 41st to 59th birthdays in a fund earning 10% compounded annually. How much should each of these amounts be?

LET 41 st  birthday = year 0 A = ₱18,000

60 th   59 th  

41 st  

i = 0.10 compounded annually A

70 th  

 

 A

−1 1

(1 + 0.10 )1 9−1

 1−( 1 + 0.10 )

=18000 11 1−( 1 + 0.10 ) −

 A =18000

 A = ₱  2,2 2,285. 85. 25

3

. A company wil willl borrow a loan to fi finance nance a 10-year proje project ct that will require aan n init initial ial ins install tallation ation ccost ost of ₱2,500,000. After 2 years another P500,000 and a regular annual upkeep cost of ₱75,000 paid ev ery e nd of the year. If the interest rate of the loan is 2 % per annum, what amount should be loan loaned? ed? ₱75,000 ₱2,500,000

₱500,000

P i = 0.02 per annum  P=

2500000 + 500000 + ( 75000∗9 ) 10

 P= ₱  3,014,780.00

4 . A busine businessman ssman has to set settle tle a debt of 4 equal se semi-a mi-annual nnual payment paymentss of ₱50,0 ₱50,000 00 at 9% rat ratee of inte interest rest compounded semi-annually. However, he was not able to do so. Instead, he negotiated with the bank to settle it into 8 quarterly payments at the s ame 9% interest rate but compounded quarterly. How much much should the new payments be?

₱50,000

i = 0.09 compounded semi-annually

i = 0.09 compounded quarterly A

 

50000

(

1+

 )

0.09 2

0.09 2

 A = ₱  29,516.23

4

−1

(

1− 1 + = A 

4

0.09 4

−8

 )

0.09