Sancha wants to invest $18,000. She is considering two investing options.
Option 1: Invest with a 9% simple interest rate over a 12-year period.
Option 2: Invest with an 8% compound interest rate over a 10-year period, with interest compounded monthly.
Compare the two options to determine which one offers Sancha more financial advantages. Find the final amount of the investment of the better investing option.
Round the answer to two decimal places as needed.(1 point)
Option
offers Sancha more financial advantages. With this option, the final amount of the investment is $
.
To find the final amount of Option 1, we can use the formula for simple interest:
Final Amount = Initial Investment + (Initial Investment × Interest Rate × Time)
Plugging in the given values, we get:
Final Amount = $18,000 + ($18,000 × 0.09 × 12)
Final Amount = $18,000 + ($18,000 × 1.08)
Final Amount = $18,000 + $19,440
Final Amount = $37,440
To find the final amount of Option 2, we can use the formula for compound interest:
Final Amount = Initial Investment × (1 + Interest Rate/100)^(Number of Compounding Periods)
Plugging in the given values, we get:
Final Amount = $18,000 × (1 + 0.08/12)^(10*12)
Final Amount = $18,000 × (1 + 0.0066667)^(120)
Final Amount = $18,000 × (1.0066667)^(120)
Final Amount = $18,000 × 1.995030035
Final Amount = $35,910.54
Comparing the two options, we can see that Option 1 offers Sancha more financial advantages. The final amount of the investment in Option 1 is $37,440.