Sanjay wants to buy a condominium in 3 yrs. He's planning to save for down payment. He plans to deposit $2500 at the beginning of each year into a savings account. The savings account pays 2.25% interest, compounded monthly.
How much money will Sanjay have at the end of 3 yrs?
To calculate the future value of Sanjay's savings at the end of 3 years, we can use the formula for compound interest:
FV = P(1 + r/n)^(nt)
Where:
FV = Future Value (the amount of money Sanjay will have at the end of 3 years)
P = Principal amount (the amount Sanjay deposits at the beginning of each year, which is $2500 in this case)
r = Annual interest rate (2.25% in this case, which needs to be converted to a decimal by dividing by 100)
n = Number of times the interest is compounded per year (monthly compounding in this case, so n = 12)
t = Number of years (3 years in this case)
Let's calculate the future value:
FV = $2500*(1 + 0.0225/12)^(12*3)
First, let's calculate (1 + 0.0225/12)^(12*3):
(1 + 0.001875)^(36)
Now, raise that to the power of 36:
(1.001875)^(36) = 1.068094573
Finally, multiply this result by the principal amount:
FV = $2500 * 1.068094573
Thus, Sanjay will have approximately $2670.24 at the end of 3 years.