Determine whether an 8.3% simple interest rate or a 7.2% compound interest rate with interest compounded monthly is the better investing option when $3,800 is invested for 4 years.Enter 1 if an 8.3% simple interest rate is the better option.Enter 2 if a 7.2% compound interest rate with interest compounded monthly is the better option.
To determine which option is better, we can compare the final amount obtained after 4 years with each interest rate.
For the first option, the simple interest formula is:
Final Amount = Principal * (1 + (Interest Rate * Time))
Plugging in the values, we get:
Final Amount = 3,800 * (1 + (0.083 * 4))
Final Amount = 3,800 * (1 + 0.332)
Final Amount = 3,800 * 1.332
Final Amount = 5,061.60
For the second option, the compound interest formula is:
Final Amount = Principal * (1 + (Interest Rate / n))^(n * Time)
Plugging in the values, we get:
Final Amount = 3,800 * (1 + (0.072 / 12))^(12 * 4)
Final Amount = 3,800 * (1 + 0.006)^48
Final Amount = 3,800 * 1.006^48
Final Amount = 3,800 * 1.334
Final Amount = 5,071.20
Comparing the two final amounts, we see that the option with the compound interest rate yields a higher value of $5,071.20. Therefore, the better investing option is the 7.2% compound interest rate with interest compounded monthly.
Thus, we enter 2.