2022 ASRJC Promo Q12

Betty received an SMS from a friend regarding a Bitcoin (BTC) investment that guarantees a fixed percentage of interest per month. Betty clicked on the link in the SMS and found out that the BTC investment has an account for each investor. An interest is added to the account at the end of each month at a fixed rate of \(11\%\) of the amount in the account at the beginning of the month.

1. Betty decides to start an investment account with \(\$1500\) on 1 Jan 2022. She invests with the intention of not withdrawing any money out of the account but just leave it for the interest to build up. Find the total profit at the end of one full year.[2]

Betty forwards the SMS to her friend, Carl, who decides to invest \(\$200\) on the first day of each month starting from 1 Jan 2022.

2. Show that the projected amount of money in Carl’s investment account at the end of \(n\) months of investment is given by \(\frac{22200}{11}\left[ {{\left( \frac{111}{100} \right)}^{n}}-1 \right]\).[3]
3. Find the projected amount of money in Carl’s investment account at the end of one year.[1]
4. Determine with clear reasons, the date on which the projected amount of money in Carl’s investment account first exceeds the projected amount of money in Betty’s investment account.[4]

Unfortunately, the BTC investment is a scam. According to the Police, victims in Singapore lost \(\$633.3\) million to scams in 2021. With public education campaigns, a researcher predicts that the amount lost to scams each year will drop by \(5\%\) of the amount lost in the preceding year.

5. If the researcher is correct in his predictions, what would be the theoretical total amount of money lost to scams from 2021 (inclusive) onwards?[2]