Question

1. You would like to save $70 000 in 10 years. To accumulate this amount, you plan to make a regular deposit with an equal amount of cash into a saving account at the end of each year. This account will earn 6% p.a interest compounded annually. Your first payment will be made at the end of this year. a. How much must you deposit annually to accumulate this amount in 10 years? b. If you decide to make a large one-off lump-sum deposit today instead of the annual deposits, how large should the lump-sum deposit be? (Assume that you can earn 6% interest annually on this deposit.) c. You would like to reach your goal of $70,000 at the end of year 8 instead of waiting for 10 years. Thus, in addition to the regular annual deposits as in question (a), you would want to make an additional deposit at the end of year 5. How much do you need to deposit to reach your $70,000 at the end of year 8? (Again, assume that you can earn 6% annual interest on this deposit.) d. How does the answer in question (a) differ if the bank pays you 6% interest compounded semi-annually and you would like to make deposits each 6 months?

Answer 1

FV = 70000$

Interest = 6% Compounded Annually

N = 10 Years

a.

P         =	A(r/n)
[(1+r/n)^nt-1]

P = 70000(0.06)/[1+0.06)^10-1]

= 5310 $

Since compounded annually the above method is used.here n = 12/12 = 1

b.Present Value = Future Value (1 + i)^-n

PV = 70000(1+0.06)^-10

Large one off sum deposit today = Present Value = 39088 $

C

P         =	A(r/n)
[(1+r/n)^nt-1]

P = 70000(0.06)/[1+0.06)^8-1]

= 7073 $

He needs to invest additional amount of $ 1762 on compared with question a)

Since compounded annually the above method is used.here n = 12/12 = 1

d.

P         =	A(r/n)
[(1+r/n)^nt-1]

P = 70000(0.06/2)/[(1+0.06/2)^2*10-1]

= 1244 $

Semiannually so n =2