Question

Find the amount accumulated after investing a principal P for t years at an interest rate compounded annually and for simple interest at the same rate. P = $2300, r = 2%, t = 5 years.

A. $2503.45
B. $2418.00
C. $2600.00
D. $2250.00

Answer 1

After calculating, the amount accumulated with simple interest for a $2300 principal at 2% over 5 years is $2530.00. Using compound interest, the amount is $2539.38. None of the options given matches these exact values, but the closest match for simple interest is Option B and for compound interest is Option A after rounding.

Step-by-step explanation:

To find the accumulated amount with simple interest, we use the formula:

1. Principal + (principal × rate × time)

For a principal of $2300, a rate of 2% (which is 0.02 as a decimal), and a time period of 5 years, the calculation is:

$2300 + ($2300 × 0.02 × 5) = $2300 + $230 = $2530.00
To find the accumulated amount with compound interest, we use the formula:

1. Principal(1 + interest rate)time

Using the same principal, rate, and time, the calculation is:

$2300(1+0.02)5 = $2300(1.10408) = $2539.38
Comparing these values to the options given, we can see that neither simple nor compound interest calculations match any of the provided choices exactly. However, the closest match for simple interest is Option B ($2418.00), and for compound interest, after rounding, would be Option A ($2503.45).