Question

When Ram was 16 years old, he deposited a certain sum of money in a bank at the rate of 10% p. a. Compounded annually. After his balance became 121 /700 times of the initial principal, he deposited 1/70 of the existing balance in the same account. After 1 year to this deposition, the bank changed it's policy to give interest at 20%p.a. simple interest. At the age of 24 years, Ram planned to start a business so, he withdrew all the money from his account. He found that the withdrawn amount was Rs. 359 less than thrice of the initial principal. Then,

1) Find the sum deposited by Ram at the age of 16 years.
2)The amount withdrawn from the bank was not enough so, he borrowed a loan of Rs. 1,10,000 from the bank and agreed to pay within 4 years, at a rate of 15% pa. compounded annually. He paid the interest of the first year at the end of the 1st year. He cleared his debt by paying equal installments in next year 2 years and 1 year. Find the total interest paid by him to the bank.
3) For how many years, he should have waited -to start the business so that he need not borrow an entra loan?​

Answer 1

Explanation:

Let the principal deposited by Ram at the age of 16 be P.

After the balance became 121/700 times of the initial principal, we have:

(121/700)P = P(1 + 10/100)^n

where n is the number of years for which the amount is compounded annually.

Simplifying the above equation, we get:

n = log(121/700)/log(1.1)

After Ram deposited 1/70 of the existing balance, his new balance became:

(121/700)P + (1/70)[(121/700)P] = (121/700)P(1 + 1/10)

After 1 year of this deposit, the new balance became:

(121/700)P*(1 + 1/10)(1 + 20/100) = (121/700)P(11/10)*(6/5) = (363/350)P

Given that this amount is Rs. 359 less than thrice of the initial principal, we get:

(363/350)P = 3P - 359

=> P = Rs. 2450

Therefore, the sum deposited by Ram at the age of 16 years was Rs. 2450.

The loan amount borrowed by Ram from the bank is Rs. 1,10,000 at a rate of 15% p.a. compounded annually for 4 years. Let the interest paid by Ram at the end of the 1st year be I1.

The amount to be paid by Ram at the end of the 1st year = 1,10,000*(1 + 15/100) = Rs. 1,26,500

Out of this, Ram pays only the interest amount, i.e., I1.

The remaining amount to be paid by Ram after the 1st year = 1,26,500 - I1

This amount is to be paid in 3 years, at a rate of 15% p.a. compounded annually.

Let the equal installments to be paid by Ram for the next 3 years be X.

Therefore, we have:

X*(1 + 15/100)^3 + X*(1 + 15/100)^2 + X*(1 + 15/100) = 1,26,500 - I1

Solving the above equation, we get:

X = Rs. 36,285.47

Therefore, the total interest paid by Ram to the bank is:

I1 + 3X - 1,10,000 = I1 + 336,285.47 - 1,10,000 = Rs. 59,856.41

To avoid borrowing an extra loan, the withdrawn amount should be equal to or greater than the amount required to start the business.

The withdrawn amount is given by:

3P - 359 = 3*2450 - 359 = Rs. 6891

Therefore, Ram should have waited for the amount in his bank account to become Rs. 6891 or more, which would take n years, where:

(121/700)2450(1 + 10/100)^n >= 6891

Solving the above equation, we get:

n >= 4.52

Therefore, Ram should have waited for at least 5 years to start the business, to avoid borrowing an extra loan.