To calculate the future value of the savings account after 65 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the savings account
P = the initial deposit ($370)
r = the annual interest rate (2% or 0.02)
n = the number of times the interest is compounded per year (quarterly, so n = 4)
t = the number of years (65)
Plugging in the values:
A = 370(1 + 0.02/4)^(4*65)
Calculating the exponent:
A = 370(1 + 0.005)^(260)
A = 370(1.005)^(260)
Using a calculator, we find:
A ≈ 370 * 7.673
A ≈ $2,839.81
Therefore, the amount of money in the account after 65 years would be approximately $2,839.81.
To determine if the savings have tripled, we can compare the final amount with three times the initial deposit:
3 * 370 = $1,110
Since $2,839.81 is greater than $1,110, the savings have indeed tripled in that time.