Question

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).

Answer 1

It will take you 79 years to buy the yacht

Step-by-step 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