Question

suppose you invest £105 savings at the start of each month with interest paid monthly and compounded with a savings rate of 3%. Work out total savings for 6 and 12 months. Must use formulae for compound interest and Geometric series to calculate total investment

Answer 1

The following expression gives the total amount at the end of 6 months:

S= 105(1.03)⁶ +105(1.03)⁵.......105(1.03)

This is a geometric series with a =105(1.03)⁶ n=6 months.The monthly rate of interest is 3%. The multiplicative factor is x=1/1.03

The future value at the end of six months is:

F.V.= 105(1.03)⁶ (1-1/1.03⁶)/ (1-1/1.03) =£689.38

F.V. at the end of 6 months=£689.38

Similarly the future value at the end of 12 months will be:

F.V.= 105(1.03)¹² (1-1/1.03¹²) / (1-1/1.03) =£1553.28

Total savings at the end of 6 months =£689.38

Total savings at the end of 12 months= £1553.28