Final answer:
The total account balance when payments begin on the loan with an initial principal of $2,500 and a monthly-compounded interest rate of 4.03% after 12 months is approximately $2,602.19. The closest given answer is $2,602.63.
Step-by-step explanation:
The question is asking for the total account balance of a personal loan after 12 months when no payments have been made, with the interest being compounded monthly. To calculate this, we use the compound interest formula:
A = P(1 + r/n)^{nt}
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial sum borrowed).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per unit t.
- t is the time the money is invested or borrowed for, in years.
In this case, P is $2,500, r is 4.03% or 0.0403 in decimal form, n is 12 (since the interest is compounded monthly), and t is 1 year (since we're looking at the balance after 12 months).
By substituting these values into the formula, we calculate the new balance:
A = $2,500(1 + 0.0403/12)^{12^1}
A = $2,500(1 + 0.003358333)^{12}
A = $2,500(1.003358333)^{12}
A = $2,500(1.040875896)
A = $2,602.19 approximately
The total account balance when payments begin is approximately $2,602.19. Hence, the closest answer from the given options is c. $2,602.63. It is important to note that the final answer may slightly vary due to rounding in the intermediate steps.