Probset-13579 - Might be helpful. PDF

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Summary

What is the annual rate of interest if P265 is earned in four months on an investment of P15,000? Given: P = P15,000 I = P265 Find: in = 4 12= 13Solution:F = P + I F =15,000+ 265F =15,F = P ( 1 +¿)i =FP− 1ni =15,15,− 113i =0∨5 % If you borrow money from your friend with simple interest of 12%, find ...

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1. What is the annual rate of interest if P265 is earned in four months on an investment of P15,000? Given: P = P15,000 n=

I = P265

Find: i

4 1 = 12 3

Solution:

F=P+ I F=15,000+265 F=15,265

F = P (1+¿) F −1 P i= n 15,265 −1 15,000 i= 1 3 i=0.053 ∨5.3 %

3. If you borrow money from your friend with simple interest of 12%, find the present worth of P20,000, which is due at the end of nine months. Given: F = P20,000 i = 12%

Solution:

F = P (1+¿) P= P=

F 1+¿ 20,000 3 1+ (0.12) 4

P=18,348.62

n=

9 3 = 12 4

Find: P

5. A man wishes his son to receive P200,000 ten years from now. What amount should he invest if it will earn interest of 10% compounded annually during the first 5 years and 12% compounded quarterly during the next 5 years? Given: F = P200,000

n = 9/12

Compound interest for first 5 years: i = 10%

n=5

Compound interest for 6 to 10 years: i = 12%/4 = 3% n = 5×4 = 20 Find: P1 Solution:

P2=F (1+i)−n −20

P2=200,000(1+0.03) P2=110,735.15

P1=P2 (1+i)−n P1=110,735.15( 1+ 0.10)−5 P1=68,757.82

7. At a certain interest rate compounded semiannually, P5,00 will amount to P20,000 after 10 years. What is the amount at the end of 15 years?

Given: P = P5,000 F1 = P20,000 n1 = 10

n2 = 15 m=2

Find: F2

Solution: Solve for r,

( )

F1=P 1+

r m

mn

2 (10 )

( )

P20,000=P 5,000 1+

r 2

r 1+ =1.071773463 2 r=0.1435469251 Solve for F2,

(

0.1435469251 2

F 2= P 5,000 1+

2 (15 )

)

F 2= P 40,000

1

9. A woman borrowed P3, 000 to be paid after

1 2

years with interest at 12% compounded

semiannually and P5, 000 to be paid after 3 years at 12% compounded monthly. What single payment must she pay after

3

1 2

years at an interest rate of 16% compounded quarterly to settle the two

obligations?

Given: P1 = P3,000 r1 = 12% n1 =

1

1 2

m1 = 2

P2 = P5,000

r3 = 16%

r2 = 12%

1 n3 = 3 2

n2 = 3

m3 = 4

m2 = 12

Solution: Solve for F1,

( )

F1=P 1+

(

r m

F1=P 3,000 1+

mn

.12 2

)(

211 2

)

F1=P 3,573.048 Solve for F2,

( ) .12 F =P 5,000 ( 1+ 12 ) F2 =P 1+

r m

mn

12 ( 3 )

2

F2 =P 7,153.844 Solve for F3,

Find: F3

m (n 3−n 1 )

( )

F3 = F1 1+

(

F3 =P3,573.048 1+

r m

0.16 4

)

(

m(n 3 −n 2)

( )

+ F 2 1+

r m

)+P 7,153.844

1 4 3 1 −1 2 2

F3 =P 4,899.963+P7,737.598 F3 =P12,637.56

(

1+

0.16 4

)(

)

4 3 1 −3 2...