Answer to Question #156990 in Financial Math for Wachira Ann Wangari

Question

a) A 8-month loan is repayable by singly payment of kshs 120,000. If the loan is issued at a rate of commercial discount of12% per annum, how much was initially lent to the borrower?

b). A company is due to receive a payment of kshs 300,000 from a customer in 3 months time. To smooth it's cash flows the company would prefer to receive the payment immediately and has agreed to transfer it's entitlement to this payment to a third party(a discount house) in return for an immediate payment. Calculate using a rate of commercial discount of 16% per annum. How much will the immediate payment by the discount house be?

c) Given a payment of kshs 2,000,000 due in 5years time, calculate the present value

I) simple interest of 3% per annum

II) simple discount of 3% per annum

III) compound interest of3% per annum

Answer 1

a)

A = P + (prt),

t= 8/12

A=120000

r= 12

p?

120000=p+(p*12/100*8/12)

120000 = p + 0.08p

120000 = 1.08p

p=120000/1.08

answer = ksh 111,111.11

b)

I=P_ort

A=P_o +I=P_O+ P_ort=P_o(1+rt)

 I is the interest

 A is the end amount principal plus interest

P_O  principal

r is the interest rate in decimal form

t is time

A=P_o +I=P_O+ P_ort=P_o(1+rt)

  =300000(1+16÷12/100×3)

    =300000(1+0.013×3)

     =300000×1.039

       answer =Ksh.311700

c)

FV=PV(1+i)ⁿ

FV= 2000,000

PV=?

i=3% =0.03

n=5

simple interest

Fv=PV(1+rt)

2000000 = PV(1+0.03*5)

PV=2000000/1.15

answer = 1,739,130.434

simple discount

2000,000 = PV(1+.03)⁵

PV=2000000/1.03⁵

answer pv = ksh1,725,217.568

compound interest

2000,000 = PV(1+.03)⁵

PV=2000000/1.03⁵

answer pv = ksh1,725,217.568