Question

2.You decide to start saving for your retirement, in 25 years time. Today you make an initial lump sum payment of 10,000, then decide to save 500 per semester and expect an average return of 6.6%(comp.semesterly or semiannually). How much will you have in the end, assuming you pay the money in the beginning of each semester? 3.Your bank has just launched a savings scheme which pays an interest at 5.15% monthly compounded, over 10 years. If you invest 100 at the end of each month, how much will you have at the end of those 10 years? 4.If you invest 50,000 a financial product that offers a 3% compounded monthly, for how long(number of months) you should keep that money invested there to finally get the double of what you initially invested?

Answer 1

2)

future value of annuity due= payment per period * [(1+i)^n - 1]/i *(1+i)

i = interest rate per period

n = number of periods

future value = 10000*(1+3.3%)^50 + 500 * [(1+3.3%)^50 - 1]/3.3%

= 112369.05

3)

future value of annuity= payment per period * [(1+i)^n - 1]/i  

i = interest rate per period

n = number of periods

future value = 100 * [(1+(5.15%/12))^120 - 1]/(5.5%/12)

= 14657.35

4)

Present value = Future value/(1+i)^n

i = interest rate per period

n= number of periods

=>

50000 = 100000/(1+(3%/12)^n

=>

n = 277.61 months

= 23.13 years