Question

Compound Interest

22.) You borrow 1,000,000 for one year from a friend at an interest rate of 1% per month instead of taking a loan from a bank at a rate of 13% per year. Compare how much money you will save or lose on the transaction.

24.) John expects to receive Php 20,000 in 10 years. How much is the money worth now considering interest at 6% compounded quarterly?

25.) A man who won P 500,000 in a lottery decided to place 50% of his winning in a trust fund for the college education of his son. If the money will earn 14% per year compounded quarterly, how much will the man have at the end of 10 years when his son will be starting his college education?

26.) Rex borrowed a certain amount on October 1990 from Jason. Two years later, Rex borrowed again from Jason an amount of P500. Rex paid P200 on October 1993and discharged his balance by paying P700 on October 1995 What was the amount borrowed by Rex on October 1990 if the interest rate is 8% compounded annually?

Answer 1

a)Amount if rate of interest=13%

A=P(1+r/n)^nt

1000000(1+.13/1)^1

=1130000

For rate = 1% monthly or 12% annually

1000000(1+.01)^12

=1126825

So he will save 1130000-1126825= 3175 on getting the loan from his friend.

b) Present value= Future value/(1+i)^mt

Where I= rate of interest per period ( rate of interest/no of times compounded)

M is no of times compounded

t is no of years

Therefore PV= 20000/(1+.06)^40

No of years is 10 and m = 4

Therefore 20000/10.2857

= 1944.44

c)

Future Value=Present Value*(1+i)^mt

PV is 50% of 500,000= 250,000

Therefore

=250,000*(1+14/100)^40

250,000*(1.035)^40

= 250,000*3.95925

= 989,814.93

Money he will have after investing in the trust fund is 989814.93

d)

In year 1990 he borrowed x amount of money

In year 1992 he borrowed 500

In year 1993 he paid back 200

And in 1995 he cleared all dues by paying 700

Therefore accordingly

We can form an equation using compound interest that

X(1+.08)^5 + 500(1+.08)^3= 200 + 700

or X(1.08)^5=900-629.86.  

{ 500*1.259= 629.86}

Therefore X= 270.14/(1.08)^5

X= 183.85

n is taken to be 5 and 3 because all the dues were cleared within 5 and 3 years of borrowing respectively.

So Rex borrowed 184P from his friend.