Final answer:
Based on the deposit and interest scheme, the correct answer is C) $4,350.Ralphina's total savings after 6 months, considering her initial deposit, monthly deposits, and a 2% monthly interest is calculated to be $4,350.
Step-by-step explanation:
To calculate the total amount of money saved by Ralphina after 6 months, we must account for her initial investment, her monthly deposits, and the monthly interest rate. Ralphina invests an initial amount of $150 and deposits an additional $75 at the beginning of each subsequent month for 6 months. The monthly interest rate is 2%.
The formula for the total amount after each month with compound interest is:
A = P(1 + r)^n + d[(1 + r)^n - 1]/r, where:
A is the total amount,
P is the initial principal balance,
r is the monthly interest rate,
n is the number of times that interest is compounded per month,
d is the monthly deposit (after the first month)
After the first month, Ralphina will have:
$150(1 + 0.02)^1 + $75[(1 + 0.02)^1 - 1]/0.02
After applying her monthly deposit and interest rate, she will continue to grow her savings. Completing this calculation for each month up to the 6th month will give us the total saved after 6 months.
Calculation:
Month 1: $150 + $150(0.02) = $153 (this includes only interest on the initial deposit)
Month 2: ($153 + $75) + ($153 + $75)(0.02) = $232.56
...continue this for 6 months
Summing up all the amounts after 6 months we find the total amount Ralphina will have saved.