To calculate the future value of each investment, we use the formula:

$FV = PV \times (1 + \frac{r}{n})^{n \times t}$

Where:

• $FV$: Future Value
• $PV$: Present Value
• $r$: Annual nominal interest rate (in decimal form)
• $n$: Number of compounding periods per year
• $t$: Time in years (number of compounding periods divided by $n$)

Let's calculate each one:

1. $21,400 at 4.75% Annually for 12 years

$r = 0.0475, \; n = 1, \; t = 12$ $FV = 21,400 \times (1 + \frac{0.0475}{1})^{1 \times 12}$ $FV = 21,400 \times (1.0475)^{12} \approx 21,400 \times 1.747422$ $FV \approx 37,393.43$

2. $40,100 at 1.50% Semi-annually for 24 periods

$r = 0.015, \; n = 2, \; t = \frac{24}{2} = 12$ $FV = 40,100 \times (1 + \frac{0.015}{2})^{2 \times 12}$ $FV = 40,100 \times (1.0075)^{24} \approx 40,100 \times 1.196682$ $FV \approx 48,016.90$

3. $14,000 at 5.50% Quarterly for 36 periods

$r = 0.055, \; n = 4, \; t = \frac{36}{4} = 9$ $FV = 14,000 \times (1 + \frac{0.055}{4})^{4 \times 9}$ $FV = 14,000 \times (1.01375)^{36} \approx 14,000 \times 1.648666$ $FV \approx 23,081.33$

4. $37,000 at 3.75% Monthly for 48 periods

$r = 0.0375, \; n = 12, \; t = \frac{48}{12} = 4$ $FV = 37,000 \times (1 + \frac{0.0375}{12})^{12 \times 4}$ $FV = 37,000 \times (1.003125)^{48} \approx 37,000 \times 1.161184$ $FV \approx 42,963.82$

Final Results

1. $37,393.43
2. $48,016.90
3. $23,081.33
4. $42,963.82

Would you like further explanation on any of these?

Related Questions

1. How does compounding frequency affect future value?
2. What is the difference between nominal and effective interest rates?
3. Can future value calculations be applied to variable interest rates?
4. What happens if the compounding frequency is continuously compounded?
5. How can we determine the time needed to reach a target future value?

Tip:

The more frequent the compounding, the higher the future value, assuming the same nominal interest rate.