Question

Commencing January 1 2022 Narelle plans to deposit $500 at the beginning of each month into an investment fund. The first deposit will be made on January 1 2022. Narelle predicts that the rate of return on this fund will be j12=5.63% from 1 January 2022 to 30 June 2022 and j12=5.96% from 1 July 2022 to 31 December 2022. If we assume these deposits are made at regular intervals, what will the balance of this account be on 31 December 2022?

a. 6189.09
b. 6194.25
c. 6102.23
d. 6164.49

Answer 1

The calculation of the investment account balance on December 31, 2022, requires annuity due formulas with varying interest rates and cannot be directly derived from given examples designed for lump sum investments.

Step-by-step explanation:

The student wishes to know the balance of an investment account after making monthly deposits of $500 with varying interest rates partway through the year. To calculate this, we must consider each period of deposits separately due to the change in interest rates.

For January 1, 2022, to June 30, 2022, with an interest rate of 5.63% per annum (compounded monthly), the formula for the future value of an annuity due can be used. Subsequently, for deposits from July 1, 2022, to December 31, 2022, the new interest rate of 5.96% per annum (compounded monthly) will apply. However, to accurately provide an account balance, a specific financial formula that accounts for regular deposits and a change in interest rates should be used to compute the balance.

The question cannot be answered with the given examples as they are geared towards single lump sum investments, not regular monthly deposits with changing interest rates. Therefore, the question requires a method that takes into account annuity due calculations with a change in the periodic interest rate.