A deposit of $10,000 increased to $12,500 in 5 years. Determine the annual rate of interest used and calculate the balance at the end of year four.
A) $11,954
B) $12,254
C) $13,954
D) $14,254
E) $15,954

Question

Quizplus · Accepted Answer

The deposit grew from $10,000 to $12,500 in 5 years, which is an increase of $2,500. To find the annual interest rate, we can use the formula for simple interest: $I = P \times r \times t$, where $I$ is the interest, $P$ is the principal amount, $r$ is the rate of interest per year, and $t$ is the time in years. Rearranging the formula to solve for $r$, we get $r = \frac{I}{P \times t}$. Substituting the given values, $r = \frac{2500}{10000 \times 5} = \frac{2500}{50000} = 0.05$, or 5% per year.To calculate the balance at the end of year four, we use the formula for the future value of a single sum: $FV = P(1 + rt)$, where $FV$ is the future value, $P$ is the principal amount, $r$ is the rate of interest per year, and $t$ is the time in years. Substituting the given values, $FV = 10000(1 + 0.05 \times 4) = 10000(1 + 0.2) = 10000 \times 1.2 = 12000$. However, since the question seems to imply compound interest due to the discrepancy in the calculation, we should consider the compound interest formula, which wasn't directly used in the explanation. Given the options and the context, the closest match to a reasonable outcome for year four under typical compound interest scenarios is option A, but the exact calculation method and the correct interpretation of the interest type (simple vs. compound) were not fully detailed in the explanation provided.

A Deposit of $10,000 Increased to $12,500 in 5 Years