The number of days from May 3rd to July 15th is 28 (May) + 30 (June) + 15 (July) = 73 days. Simple Interest = (Principal * Rate * Time) / 100. Using 73/365 years, SI = (500 * 6 * 73) / (100 * 365) = 3000 / 500 = 6.
712
At what annual compound interest rate will a principal of Rs. 1,000 grow to Rs. 1,331 over a period of 3 years?
Using the compound interest formula A = P(1 + r/100)^n, we have 1331 = 1000(1 + r/100)^3. Dividing by 1000 gives 1.331 = (1 + r/100)^3. Taking the cube root of 1.331 results in 1.1. Therefore, 1 + r/100 = 1.1, which simplifies to r/100 = 0.1, meaning the rate is 10% per annum.
713
A loan of Rs. 1000 was taken on January 1, 1997, at a simple interest rate of 10% per annum. If the total repayment amount was Rs. 1020, on what date was the loan settled?
The interest earned is Rs. 20. Using the simple interest formula I = (P * R * T) / 100, we have 20 = (1000 * 10 * T) / 100, which simplifies to T = 0.02 years. Converting 0.02 years to days (0.02 * 365) gives approximately 7.3 days. Counting 73 days from January 1st leads to March 14th, 1997.
714
A town's population increases by 5% annually. Given the current population is 4,410, what was the population two years ago?
Using the compound growth formula P = P0(1 + r)^n, we set 4410 = P0(1 + 0.05)^2. Solving for P0 gives 4410 / 1.1025, which equals 4000. Thus, the population two years ago was 4,000.
715
Calculate the compound interest on a principal amount of Rs. 2000 at an annual interest rate of 5% compounded annually for a period of 2 years.
To find the compound interest, we use the formula A = P(1 + r/n)^(nt). Here, P = 2000, r = 0.05, and t = 2. The amount A = 2000 * (1.05)^2 = 2000 * 1.1025 = 2205. The compound interest is the total amount minus the principal, which is 2205 - 2000 = Rs. 205.
716
Calculate the annual interest rate required for a principal sum of Rs. 5000 to grow to Rs. 6000 over a period of 4 years.
To find the rate, we use the simple interest formula. The total interest earned is Rs. 1000 (6000 - 5000). Using the formula Interest = (Principal * Rate * Time) / 100, we get 1000 = (5000 * R * 4) / 100. Solving for R gives 1000 = 200R, which results in R = 5%.
717
A sum of money is lent at a simple interest rate. If the principal amount triples in 16 years, what is the annual interest rate?
If a sum triples, the interest earned is twice the principal (2P). Using the simple interest formula I = PRT/100, we have 2P = P * R * 16 / 100. Solving for R gives R = 200 / 16, which equals 12.5 percent.
718
Mr. Khalid borrowed Rs. 10,000 at a simple interest rate of 8% per annum for 6 years. What is the total amount he must repay?
First, calculate the simple interest using the formula SI = (P * R * T) / 100. Substituting the values: (10,000 * 8 * 6) / 100 = 4,800. The total amount to be repaid is the principal plus the interest: 10,000 + 4,800 = 14,800.
