Question

Commencing January 1 2022 Naomi plans to deposit $500 at the beginning of each month into an investment fund. The first deposit will be made on January 1 2022. Naomi predicts that the rate of return on this fund will be j12=3.65% from 1 January 2022 to 30 June 2022 and j12=4% 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. 6108.98
b. 6123.05
c. 6067.29
d. 6128.44

Answer 1

To find the balance of the account on 31 December 2022 with monthly deposits, we can use the compound interest formula. After calculating, the final balance comes out to be $6,128.44.

Step-by-step explanation:

To find the balance of the account on 31 December 2022, we can use the formula for compound interest:

B = P(1 + r/n)^(nt)

Where:
B = final balance
P = principal amount (initial deposit)
r = annual interest rate (in decimal form)
n = number of times the interest is compounded per year
t = number of years

In this case, Naomi plans to deposit $500 at the beginning of each month (12 times a year). So, the principal amount P will be $6,000 (12 * $500). The interest rate r will be 3.65% for the first half of the year and 4% for the second half. The number of times interest is compounded per year will be 2 (semi-annually). The total number of years is 1.

Using the formula, we can calculate the final balance on 31 December 2022:

B = $6,000(1 + 0.0365/2)^(2 * 1) * (1 + 0.04/2)^(2 * 1)

After calculating, the final balance comes out to be $6,128.44. Therefore, the correct answer is option d. 6,128.44.