Finance and Accounting Assignment Math Problem Example | Topics and Well Written Essays - 750 words

Finance and Accounting Assignment - Math Problem ExampleSince in this case, the retribution is done at the beginning of the period every time, and so it is a case of an warm rente as apiece yearly payment is allowable to compound for an additional year as compared to the normal annuity case. In this context, incoming nurse of Annuity = A (1+i) n -1 / i (Finance Formulas., n.d.) Where, A= one-year payment, i= liaison rate per year, n= number of periods As in this case, each yearbook payment is completed at the start of each period, the same is allowed to compound for one extra period and hence its future value would be the product of value of a matching normal annuity and (1+ sake rate). in store(predicate) Value of Annuity overdue = (1+i) * A (1+i)n -1 / i (Finance Formulas., n.d.) The sixty-fifth birth solar day is the day the somebody wants to have $2 million in the savings account. It should also be kept in mind that a payment is made rase on the last day i.e. on the 65th birthday. This last payment does not get a chance to be compounded and has to be plainly added to the compounded value of the earlier made 35 payments. In the Future Value of Annuity Due formulae, it has to be noted that the last cash payment is made one year prior to the destroy of the 35th year. Keeping in mind that a payment will be made even on the last day of 35 year period, the formulae for calculating the required annual payment would be, Future Value, FV = (1+i) * A (1+i)n -1 / i + A A = F/ ((1+i)n-1)/i * (1+i) +1 It is decided that the person take $2 million at the end of 35 years period, so in this scenario the Future Value would be $2 million. In this case, FV= $2000000, i= 5%, n= 35 years. Putting these values in the above equation, Annual Payment, A = 20,868.91 = $ 20,870 (approx) Thus, the person has to put aside $ 20,869 (approx) each year to make trusted that he has $ 2 million in the savings account on the 65th birthday. Problem 36 The person realizes th at since the income would enlarge over the years it would be advisable to save less now and much in the later years. Thus, instead of putting the same numerate aside, the person has altered his plans to let the amount to be set aside grow by 3% per year. This is a case of growing annuity which is similar to annuity as both ends after a certain period, however, growing annuity payments increase at a fixed constant rate unlike the annuity. It should be noted that since the first annual payment to the savings account is made today and continuing to do so on each birthday up to as well as including the 65th birthday, the number of periods would be 36. The formula for Future Value of Growing Annuity is, FV = A (1+i)n (1+g)n / (i-g) (Finance Formulas., n.d.) Where A= First payment, i= interest rate, g= growth rate, n= number of periods Hence, The First Payment, A = FV * (i-g)/ (1+i)n (1+g)n Here, FV= $2000000, i = 5%, g = 3%, n = 36. Putting these values in the above equation, Fir st Payment = 13,823.91 = $ 13,824 (approx) Thus, the person will have to put $ 13,824 (approx) into the savings account today and keep on increasing the deliver the goods payments at a growth rate of 3% per year in order to get $ 2 million in the savings account on the 65th birthday. References Finance Formulas. (n.d.). Future Value of Annuity. Retrieved July 14, 2011, from