Question

Find the value of $100 invested each month at 6.25% compounded monthly after 4 years.

Answer 1

The future value of $100 monthly investments at 6.25% compounded monthly after 4 years is approximately $5,425.53.

Let's calculate the future value of the monthly investments using the formula for the future value of an ordinary annuity:

`\[ FV = P \left( ((1 + r)^(nt) - 1)/(r) \right) \]`

Where:

-
`\( P = $100 \) (monthly investment),`

-
`\( r = (0.0625)/(12) \) (monthly interest rate),`

-
`\( n = 12 \) (monthly compounding),`

-
`\( t = 4 \) years.`

`\[ FV = 100 \left( ((1 + (0.0625)/(12))^(12 * 4) - 1)/((0.0625)/(12)) \right) \]`

After performing the calculation:

`\[ FV \approx 100 \left( ((1 + 0.005208333333)^(48) - 1)/(0.005208333333) \right) \]`

`\[ FV \approx 100 \left( ((1.005208333333)^(48) - 1)/(0.005208333333) \right) \]`

`\[ FV \approx 100 \left( (1.28203723108 - 1)/(0.005208333333) \right) \]`

`\[ FV \approx 100 \left( (0.28203723108)/(0.005208333333) \right) \]`

`\[ FV \approx 100 * 54.2552504 \]`

`\[ FV \approx $5,425.525 \]`

Therefore, the future value of the monthly investments after 4 years at a 6.25% monthly interest rate compounded monthly is approximately $5,425.53.