Question

Alvin Miller, owner of Miller Garage, estimates that he will need 6. $18,000 for new equipment in 20 years. Alvin decided to put aside the money today so it will be available in 20 years.Sound Bank offers Alvin 12% interest compounded semiannually. How much must Alvin invest today to have $18,000 in 20 years

Answer 1

Alvin must invest approximately $2,364.50 today to have $18,000 in 20 years with a 12% interest rate compounded semiannually.

Explanation:

To determine how much Alvin must invest today to have $18,000 in 20 years with a 12% interest rate compounded semiannually, you can use the formula for compound interest:

FV = PV x ( 1 + ( r / n ) ) ^ nt

Where:

• FV is the future value (in this case, $18,000).

• PV is the present value or the amount Alvin needs to invest today.

• r is the annual interest rate (12% or 0.12 as a decimal).

• n is the number of times interest is compounded annually (semiannually, so n = 2).

• t is the number of years (20 years).

Now, plug in the values:

Simplify the exponent:

Finally, solve for PV

Using a calculator, calculate the present value:

PV ≈ \frac{18,000}{7.61225503} ≈ $2,364.50

So, Alvin must invest approximately $2,364.50 today to have $18,000 in 20 years with a 12% interest rate compounded semiannually.