Question

Victoria opens a savings account with an initial deposit of $5,000, earning 4.9% compound interest each quarter. After 28 years, with quarterly deposits of $200, what is the estimated final balance?

A) $12,345
B) $15,678
C) $18,902
D) $22,431

Answer 1

To calculate Victoria's final balance, the compound interest formula must be used. Given the complexity of the calculation with additional contributions, a financial calculator or a specific application is usually employed to determine the exact amount.

Step-by-step explanation:

Victoria's final balance in her savings account after 28 years with an initial deposit of $5,000, earning 4.9% compound interest each quarter and with quarterly deposits of $200, can be estimated using the compound interest formula:
A = P(1 + r/n)^(nt) + PMT [(1 + r/n)^(nt) - 1] / (r/n)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount ($5,000)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested
PMT = the additional contribution every period ($200)
However, given the options provided (A, B, C, D), to accurately calculate the final balance, a financial calculator or an application designed to handle the formula for compound interest with additional contributions is typically used.