Question

1. a) Mr. Karim went worth have two debts, one of $2000 due in 18 months and another of 1500 due in 30 months. Enam as $3000. If the money is money 5% p.a. compounded semiannually, does he have enough money to pay his debts? If not how much additional money he needs? b) Mr. Rahim borrowed tk. 70000 from a bank and singed a promissory note bearing interest at 6% p.a compounded monthly for 6 months and on the maturity date he paid the interest in full. Also he signed a second note without interest for the next 6 months. He received Tk. 600000 with 8% interest rate.        I) Determine the amount of interest paid in the 1st note.       ii) What is Bank discount and find the face value of the 2nd note.

04 05

Answer 1

Solution:

1) Mr. Karim has two debts one of $2000 due in 18 months and another of 1500 due in 30 months
He has $3000
If the money is 5% p.a. compounded semiannually
then first-semester interest calculation
= 3000 * 5/100
= 150
then first semi-annual money = $3150
next, we can calculate the next interest and amount
here he has the total amount = $3150
then we can calculate the next semiannual money with him
= 3150 * 5/100
= 157.5
= $3307.5
the other way we can calculate the money with him compounded semiannually is mentioned below
Total money = principal amount (1+R/100)^2
= 3000 (1+5/100)^2
= 3000 (105/100)^2
= 3000 (21/20)(21/20)
= 3000(1.05)(1.05)
= 3307.5
hence he has the amount with him = $3307.5

Hi has two debts
one of $2000 due in 18 months then we can calculate this for one year
= 2000/18
=$1333.33
then we can round for $1333

other debt of $1500 due in 30 months
= 1500/30
= 50
= 50*12
= 600
then the total money he should pay for one year including two debts
= 1333 + 600
= $1933

hence he has enough money with him for the year ending to pay the two debts for one year.

2) Mr. Rahim borrowed tk. 70000 from a bank and signed a promissory note bearing interest at 6% p.a compounded monthly for 6 months
and on the maturity date, he paid the interest in full

calculation:

Rahim borrowed 70000 for 6% p.a. interest compounded monthly for 6 months

amount = principal amount (1+R/100)^6

= 70000 (1+6/100)^6
= 70000 (106/100)^6

= 70000 (1.06)^6
= 70000 (1.42)
= 99296

according to first note he has to pay after six months full interest = 99296 - 70000 = 29296

as per the second note he took 600000 with 8% interest rate
the calculation part is same as the above first note.
but, he took without interest for the next 6 months
hence his amount face value is same as what he took that is 600000