Your dream is to buy a yacht currently valued at $300,000. you decide to put some money aside at the end of each month so you can buy your yacht without having to take out a loan. the bank guarantees an annual percentage rate of 5.1% as long as you have an account with them. if you decide to put aside $500 each month how long will it take you to buy this yacht if the current price stays the same? (round fractional year up).

It will take you 79 years to buy the yacht

Explanation:

The future amount of an investment can be calculated using the formula;

A=P(1+r)^n

where;

A=Future value of the investment

P=Initial deposit

r=annual interest rate

n=number of years of the investment

In our case;

A=300,000 since current price remains the same

P=(500×12)=6,000 yearly

r=5.1%=5.1/100=0.051

n=unknown

replacing;

300,000=6,000(1+0.051)^n

6,000(1.051)^n=300,000

1.051^n=300,000/6,000

1.051^n=50

ln 1.051^n=ln 50

n ln 1.051=ln 50

0.0497 n=3.912

n=3.192/0.0497

n=78.65 rounded up to 79 years

It will take you 79 years to buy the yacht

cognitive overload: having a lot on your mind impairs decision-making and tends to result in the simplest, but not necessarily best, option being selected.

empathy gaps: overlooking how you might feel in a different situation can result in unnecessary purchases, such as overbuying when shopping for food on an empty stomach.

optimism and overconfidence: wearing rose-tinted glasses and having unrealistic expectations about the future can affect money management and leave you unprepared for a change in circumstance.

instant gratification: seeking instant gratification drives impulsive spending and can undermine long-term planning and savings.

harmful habits: automatic or mindless behaviour can amplify a poor financial decision as it becomes a recurring event.

social norms: we are heavily influenced by the actions of others; while this can be in certain circumstances, it also contributes to the pressure to keep up with the joneses through conspicuous consumption.

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explanation: