Deepak closes his account in an investment scheme by withdrawing Rs 10,000. 1 year ago he had withdrawn Rs 6,000. 2 year ago he had withdrawn Rs 5,000. 3 year ago he had not withdrawn any money. How much money had Deepak deposited approximately at the time of opening the account 4 year ago, if the annual simple interest is 10%?
Answer: B Let x be the money he deposited at the time of opening the account. So, after 1 year (i.e 3 year ago) it would amount to 1.1x. Since no money was withdrawn at this point, after 2 year(i.e 2 year ago) it would amount to 1.21 x At this point, the person withdrawn Rs 5,000. Hence, principal for the next year = 1.21x - 5000 Next year he earns 10% interest on this, which will amount to 1.1(1.21x - 5000) = 1.32 x - 5500 At this point he withdrawn Rs 6,000. Hence his principal for the next year be 1.32x -11500. He earns 10% interest on this, which amounts to 1.1(1.32x-11500) = 1.452 - 12650. But this is equal to 10,000 Hence, x= 15600.
Q. No. 27:
Pawan retires at the age of 60 years and his employers gives him a pension of Rs. 3600/- a year paid in half yearly installments for the rest of his life. Assuming life expectancy in India is 70 yearsand interest is 6% per annum payable half yearly, determine the present value of the pension.[Given (103)-20 = 0.55362]
Answer: D The present value of the pension is the principal amount of money which, after interestsfor different time intervals, will sum up to make 20 installments of Rs. 1800 each, which isPawan’s pension. So the Present value is equal to: => 1800/(1.03) + 1800/(1.03)2 +...............1800/(1.03)20 => 1800/1.03 *[ 1- 1/(1.03)20]/(1- 1/1.03) => 26,782.80
Q. No. 28:
At the end of the year 2002, Rajoria Institute of Management (RIM) had conducted 108 Management Development Programmes (MDP). Henceforth, every year the institute added p% of the MDP topicsat the beginning of the year and discarded q% of the outdated MDP topics at the end of the year,where p < 0 and q > 0. If RIM scheduled 108 MDP programmes at the end of the year 2006, whichone of the following is true?
Answer: C In any given year, the number of program conducted, remain the same. The number ofprogrammes added at the beginning of every year must be equal to the number ofprogrammes that are discarded at the end of every year. We must have: 108 * (p/100) = 108 * (1 + p/100)* q/100 After simplifying we get the relation p = q+ pq/100. Clearly p> q.
Q. No. 29:
Ms. Rao paid equated monthly installments (EMIs) of Rs. 25,000 each January and February towards her home lona, whose outstanding principal amount was Rs.10,00,000 in Decemner. Each EMI consists of interest on outstanding loan amount for the month and part payment of the loan amount. If interest on the loan is 12% per annum (interest is paid monthly on the demising outstanding loan), the total amount of interest that was paid by Ms. Rao in January and February was
Answer: C Interest is 12% per annum i.e. 1% per monthIn January: The loan amount is Rs.10,00,000 Interest = 1% of Rs.10,00,00 = Rs.10,000In February:The remaining loan amount is= 10,00,000 + 10,000 – 25,000 = Rs.9,85,000Interest = 1% of 9,85,000 = Rs.9850Total amount of interest paid in Jan and Feb= 10,000 + 9850 = Rs. 19850.
Q. No. 30:
A certain sum of money is invested at an interest rate of 5% per annum and a second sum, twice as large as the first, is invested at 5.5% per annum. The total amount of interest earned from the two investments together is Rs. 1000 per year and the interest is withdrawn every year. The second sum invested is:
Answer: C Let the first sum invested be Rs.x and second sum invested is Rs.2x. => (x*5*1/100) + (2x*5.5*1/100) =1000 => x= Rs 6250 Hence second sum invested will be Rs.12500.