Question

Elena is seeking to invest her regular monthly salary savings of $400 into a suitable investment. ANZ bank has offered her the best interest rate in the market, a rate of 8% p.a. compounded monthly. How much will Elena approximately accumulate in total from her ongoing savings after a period of 4 years?

Answer 1

Here Elena has monthy savings of $ 400 which she wants to invest , ANZ Bank here gives 8 % p.a which is compounded monthly.

• So let's understand what happens if only $400 is deposited for 4 years and what will be it's value after 4 years.
• We will start normal compound interest formula of A = P ( 1 + r/n ) ^nt where A is the future value of invest , P is the principal amount , r is the rate of interest , n is number times interest is compounded in a given time and t is the time period for which investment is made.
• So , now putting the value we get = A = 400 (1 + 0.08/12) ^ 12 *4 = 400 * 1.375 = $ 550
• But here Elena invest savings of her salary i.e. $ 400 each month so to know the approx value she will accumulate after 4 years we have to get the value by using compound interest formula with regular contribution or future value of a series.
• So here we will use the formula A = PMT * { [(1 + r /n ) ^nt - 1] / r/n } Where again, A is the future value of investment . PMT is the value of principal amount of monthly installments or payment, r is the rate of interest , number of times interest is compounded in a given period of time , t is the time period for which investment is made.
• So by putting the values we get A = 400{ [(1.375 ) - 1] / 0.08/12} = 400 * [ 0.375/0.00667] = 400 * 56.221 = 22488.4 APPROX.

Thus, after 4 years Elena's savings would be $22488.4 , that's quite awesome, she definitely can plan a trip to Bahamas.