Mr. Hammad is a salaried person and thinking to save for the education of his daughter. In this concern he is considering two diverse saving plans for ten years. First plan requires a deposit of Rs 5,000 every six months with annual interest rate of 6.5 percent, compounded semiannually.
However, under the second plan, he has to deposit Rs 10,000 every year with Interest rate of 7.5 percent compounded annually.
Keeping in view the given situation, you are required to answer the following
questions: a). What will be the future value of first plan at the end of 10 years?
b). What will be the future value of the second plan at the end of 10 years?
c). You are required to analyze that which plan would be suitable for him while
keeping in view his major concern: ‘The value of plan at the end of 10th year’.
d). What would be the change in your decision if the interest rate on second plan is also 6.5 percent?
(Show complete calculations and provide
To calculate the future values of the two saving plans, we can use the Future Value of an Ordinary Annuity formula:
Future Value = Payment * ((1 + Interest Rate / Number of Compounding Periods)^(Number of Compounding Periods * Number of Years) - 1) / (Interest Rate / Number of Compounding Periods)
a) For the first plan, the deposit is Rs 5,000 every six months with an annual interest rate of 6.5%, compounded semiannually. Here, we need to consider the compounding periods and the number of years.
Let's calculate the future value for this plan:
Payment = Rs 5,000
Interest Rate = 6.5% / 2 = 0.065 / 2 = 0.0325 (compounded semiannually)
Number of Compounding Periods = 2 (since the interest is compounded semiannually)
Number of Years = 10
Future Value = 5000 * ((1 + 0.0325)^(2 * 10) - 1) / 0.0325
Calculate this expression and you will get the future value of the first plan at the end of 10 years.
b) For the second plan, the deposit is Rs 10,000 every year with an interest rate of 7.5%, compounded annually. Here, we have a simple compound interest calculation.
Let's calculate the future value for this plan:
Payment = Rs 10,000
Interest Rate = 7.5% = 0.075 (compounded annually)
Number of Compounding Periods = 1 (since the interest is compounded annually)
Number of Years = 10
Future Value = 10000 * (1 + 0.075)^10
Calculate this expression and you will get the future value of the second plan at the end of 10 years.
c) To analyze which plan is suitable for Mr. Hammad, we need to compare the future values of both plans from parts a) and b). Whichever plan has a higher future value would be more suitable for Mr. Hammad as it would provide a larger amount for his daughter's education after 10 years.
d) If the interest rate on the second plan is also 6.5%, then you would need to recalculate the future value of the second plan using the updated interest rate of 6.5% instead of 7.5%. Then compare the future values of both plans to revise the decision.