Question

Mr. Andrew wants to buy a house 10 years from now. The price of the property that he is intending to buy cost N$ 1.5 million now. The inflation per year is estimated to be 5.1%, 5.3%, 5.7%, 5%, and 4.5% for the next five years and expected to remain at 4.4% for the next five years. If Andrew starts an annuity savings scheme which offers an interest of 6% per annum, then to buy the house at the end of the 10th year, what amount of money that Mr. Andrew has to save every month in the savings scheme? What will be the future value of the property with respect to the inflation?

Answer 1

Current Cost of property = C = $1.5 million = 1.5 x 1000000 = $1500000

i1 = inflation for year 1 = 5.1%, i2= inflation for year 2 = 5.3% , i3= inflation for year 3 = 5.7%, i4=inflation for year 4 = 5%,    i5 = inflation for year 5 = 4.5%, i6 = inflation per year for year 6 to 10 = 4.4%

Future value of property with respect to inflation = C(1 + i1)(1 + i2)(1 + i3)(1 + i4)(1 + i5)(1 + i6)⁵

= 1500000(1 + 5.1%)(1 + 5.3%)(1 + 5.7%)(1 + 5%)(1 + 4.5%)(1 + 4.4%)⁵

= 1500000 x 1.051 x 1.053 x 1.057 x 1.05 x 1.045 x (1.044)⁵

= 1925320.003732 x (1.044)⁵ = 1925320.003732 x 1.240230745 = 2387841.0625 = 2387841.06

Hence Future value of property with respect to inflation = 2387841.06

Rate of interest for annuity = 6% per year, monthly rate = Yearly rate / No of months in a year = 6% / 12 = 0.50%

No of years = 10

No of months = No of years x 12 = 10 x 12 = 120 months

To find the amount of money to be saved per month (at the end of each month) in annuity savings scheme we will make use of pmt function in excel

Formula to be in excel :=pmt(rate,nper,pv,-fv)

In this formula pv=0 as Mr Andrew does not make any initial lumpsum deposit to save for the house and instead saves by an annuity scheme.

Using pmt function in excel, we get monthly amount to saved in annuity scheme = 14570.7260 = 14570.73