Question

You want to buy a boat that costs today $40,000. Your plan is to save monthly amount so that you will have enough money to purchase the boat three years from now. The rate of inflation of boats is expected to be 3% per year for the near future, and your bank pays an interest rate of 3% per year compounded monthly. How much money you should save every month to buy the boat three years from now?

Answer 1

The price of boat today is $40,000 . And it's price is growing at the rate of 3% every year. So after 3 years the boat will cost equal to the current cost plus inflation rate compounded annually.

Thus $40,000 in 1st year would be = 40000 + 0.03*40000 = $41,200

$41,200 in 2nd year will be = 41200 + 0.03*41200 = $42,436

And, $42,436 in 3rd year will be = 42436 + 0.03*42436 = $43.709.08

Thus, we must save so that by 3rd year, we have $43,709.08 to buy the boat.

Let us suppose we save x dollars every month, then x compounded at annual rate of 3% on a monthly basis must give us $43709.08 after 3 years.

To calculate this we use the annuity formula:

where, "A" is our goal I.e. $43,709.08

"r" is our interest rate I.e. 3%

"n" denotes the number of times saving is compounded in a year which is 12

And "t" is the time period that is 3 years.

Plugging the values, we get value for dollars. This is the monthly amount that needs to be saved in order to purchase the boat after 3 years.