Mathematics 2000 JAMB Past Questions - Question 6: A man wishes to keep some money in savings deposit at 25% compound interest so that after 3 years he can buy a car for N150000. How much does he need to deposit now?

Correct Answer

D

Explanation

To find out how much the man needs to deposit now to have N150,000 after 3 years with a 25% compound interest rate, you can use the compound interest formula:A = P(1 + r/n)^(nt)Where: A = the future amount (N150,000 in this case) P = the principal amount (the amount the man needs to deposit now) r = the annual interest rate (25% or 0.25 as a decimal) n = the number of times the interest is compounded per year (usually, it's compounded annually, so n = 1) t = the number of years (3 years in this case)You want to find P, so you can rearrange the formula:P = A / (1 + r/n)^(nt)Now, plug in the values:P = N150,000 / (1 + 0.25/1)^(1 * 3)P = N150,000 / (1.25)^3P = N150,000 / 1.953125P ≈ N76,800Hence;The man needs to deposit approximately N76,800 now to have N150,000 after 3 years with a 25% compound interest rate.To find out how much the man needs to deposit now, we can use the formula for compound interest:A = P(1 + r/n)^(nt)Where:A = the future value of the investment (N150,000 in this case)P = the principal amount (the amount the man needs to deposit now)r = the annual interest rate (25% or 0.25 as a decimal)n = the number of times interest is compounded per year (assuming it is compounded annually, n = 1)t = the number of years (3 years in this case)Substituting the given values into the formula, we have:N150,000 = P(1 + 0.25/1)^(1*3)Simplifying the equation:N150,000 = P(1 + 0.25)^3N150,000 = P(1.25)^3N150,000 = P(1.953125)Now, we can solve for P by dividing both sides of the equation by 1.953125:P = N150,000 / 1.953125P ≈ N76,923.08Therefore, the man needs to deposit approximately N76,923.08 now in order to have N150,000 after 3 years at a compound interest rate of 25%.