If Mr. Hobbit deposits $2,000 at the end of each year for the next 10 yrs at the intrest rate of 12% per year, how much will have accumulated? How much will he have accumulated if he deposited the amounts at the beginning of each year?
An Excel spreadsheet is very helpful in these types of problems.
At the end of year 1, account=2000
At the end of year 2, account=2000*1.12+2000=4240
At the end of year 3, account=4240*1.12+2000=6748.8
Take it from here.
To find out how much Mr. Hobbit will have accumulated, we can use the formula for the future value of an ordinary annuity:
FV = P * [(1 + r)^n - 1] / r
where:
FV = Future Value
P = Periodic deposit
r = Interest rate per period
n = Number of periods
Given that Mr. Hobbit deposits $2,000 at the end (and presumably after) each year for the next 10 years at an interest rate of 12% per year, we can calculate the future value. Let's solve for both scenarios - one where the deposits are made at the end of the year, and the other where the deposits are made at the beginning of the year.
End-of-Year Deposits:
P = $2,000
r = 12% = 0.12 (decimal)
n = 10 years
FV = 2000 * [(1 + 0.12)^10 - 1] / 0.12
Calculating this equation gives us:
FV = $31,266.80
So, if Mr. Hobbit deposits $2,000 at the end of each year for the next 10 years at an interest rate of 12% per year, he will accumulate approximately $31,266.80.
Beginning-of-Year Deposits:
To calculate the future value when the deposits are made at the beginning of the year, we need to adjust the formula slightly. Instead of using the future value of an ordinary annuity formula, we use the future value of an annuity due formula:
FV = P * [(1 + r)^n - 1] / r * (1 + r)
P = $2,000
r = 12% = 0.12 (decimal)
n = 10 years
FV = 2000 * [(1 + 0.12)^10 - 1] / 0.12 * (1 + 0.12)
Calculating this equation gives us:
FV = $34,783.87
So, if Mr. Hobbit deposits $2,000 at the beginning of each year for the next 10 years at an interest rate of 12% per year, he will accumulate approximately $34,783.87.