The Pirerras are planning to go to Europe 5 yr from now and have agreed to set aside $190/month for their trip. If they deposit this money at the end of each month into a savings account paying interest at the rate of 9.5%/year compounded monthly, how much money will be in their travel fund at the end of the fifth year?
To calculate the amount of money the Pirerras will have at the end of the fifth year, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = the future value of the account after t years
P = the initial deposit or principal amount
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
Given data:
P = $190 (monthly deposit)
r = 9.5% per year = 0.095 (as a decimal)
n = 12 (compounded monthly)
t = 5 years
First, we need to calculate the total number of deposits made over the 5-year period:
Total number of deposits = number of months in 5 years = 5 years * 12 months/year = 60 deposits
Now we can calculate the future value of the account using the formula:
A = 190(1 + 0.095/12)^(12*5)
Calculating inside the parentheses:
A = 190(1 + 0.0079167)^(12*5)
Calculating the exponent:
A = 190(1.0079167)^60
Calculating the final result:
A ≈ 190 * 1.49922
Therefore, the Pirerras will have approximately $284.45 in their travel fund at the end of the fifth year.