Mr. Hammad is a salaried person and thinking to save for the education of his da

Question

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.

(I) First plan requires a deposit of Rs 5,000 every six months with annual interest
rate of 6.5 percent, compounded semiannually.
(II) 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?

Explanation / Answer

For this problem you have to use Future Value Formula = FV FV = PMT ( ((1+i)^n - 1 ) / i ) FV = future value you looking for PMT = Present value you have i = interest rate n = term or how many years its going for Note: If you are compounding semiannual or quarterly then you have to divide the " i " by the 2 for semiannual or 4 for quarterly and also need to multiple " n" by same number. A. FV = $5,000 ((( 1+.065/2)^2*10 - 1 ))/(.065/2)) FV = $5,000 ((( 1.0325)^20 - 1 ) ) / .0325) FV = $5,000 (( 1.8958 -1 ) / .0325) FV = $5,000 ( .8958 / .0325) FV = $5,000 * 27.5642 FV = $137,821 This is the amount you will have at the end of 10 years B. FV = $10,000 ((( 1+ .075) ^10 - 1 ) / .075) FV = $10,000 ( 1.0610 / .075) FV = $10,000 * 14.1471 FV = $141,471 This is the amount you will have at end of 10 year on second plan Keep in mind i didn't show all the work on this one, all you do is work your way from inside out. So work with interest and add 1 to it and then solve the power and subtract 1. Same method as A but without dividing the 2 since this is compounded annual. C. By comparing the two plans and the ending value for both, you can see second plan makes sense to go with. Money wise he is depositing same amount a year its just when this is done that makes a difference. However, they major influence here is the interest rate and that is why second plan is better since it gives most money at end of the 10 years. D. FV = $10,000 ((( 1+ .065)^10) - 1)) / .065) FV = $10,000 ( .8771 / .065) FV = $10,000 * 13.4944 FV = $134,944 This is the value of second plan with 6.5% rate With this in mind i would recommend going with first plan since you get most value for it. The reason behind this is because first plan is compounded semiannual which means more money is being earned in 1 year then the second plan so with same $ contribution you end up with more money if you are compounding more often. Hope this helps you and I know formulas are not best view since I have to write them out. But if you follow them and write them on paper it will make sense.

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.