Final answer:
To calculate Sunyu's savings after seven years, the future value of an annuity formula is applied with a monthly deposit of $175 and a 5.4% annual rate compounding monthly, leading to approximately $17,200.35.
Step-by-step explanation:
To calculate the future value of Sunyu's monthly deposits, we can use the formula for the future value of an annuity:
FV = P × rac{[(1 + r)^n - 1]}{r}
Where:
FV is the future value of the annuity.
P is the regular deposit amount.
r is the monthly interest rate (annual interest rate divided by 12).
n is the total number of deposits (number of years multiplied by 12).
In Sunyu's case:
P = $175 (monthly deposit)
r = 5.4 percent annual interest rate, so the monthly interest rate is 0.054 / 12 = 0.0045
n = 7 years × 12 months/year = 84 deposits
Now, plugging the values into the formula:
FV = 175 × rac{[(1 + 0.0045)^84 - 1]}{0.0045}
Calculating this, we find that:
FV = 175 × rac{[(1 + 0.0045)^84 - 1]}{0.0045} = 175 × rac{[1.0045^84 - 1]}{0.0045} ≈ 175 × rac{0.4423}{0.0045} = 175 × 98.2877 ≈ $17,200.35
After the last $175 deposit is made in seven years, Sunyu will have approximately $17,200.35 in her account.