Question

What sum of money now is equivalent of $8,250 two years later, if the interest is 4% per 6-month period (8% compounded semi-annually)?

Answer 1

The present value of $8,250 two years later with an interest rate of 4% per 6-month period compounded semi-annually is approximately $7,573.35.

Step-by-step explanation:

To determine the present value of $8,250 two years later with an interest rate of 4% per 6-month period compounded semi-annually, we can use the present value formula.

The present value formula is given by:

PV = FV / (1 + r/n)⁽ⁿ*ᵗ⁾

Where:

• PV is the present value (the amount we want to find)
• FV is the future value (the amount in the future)
• r is the interest rate per period (in this case, 4%)
• n is the number of compounding periods per year (in this case, 2)
• t is the number of years

Substituting the given values into the formula:

PV = 8,250 / (1 + 0.04/2)⁽²*²⁾

Simplifying the equation, we have:

PV = 8,250 / (1 + 0.02)⁴

Calculating further, we find that the present value of $8,250 two years later is approximately $7,573.35.

Answer 2

$7052.13

Step-by-step explanation:

We can calculate the present value of money equivalent of $8,250 two years later by applying present value formula

DATA

Future value = $8,250

Interest rate = 4%

Number of periods = n = 2 years x 2 times a year = 4 times

Present value =?

Solution

PV =
`(1)/(1+(interest rate)^n) futurevalue`

PV = ×\
`(1)/(1+(0.04)^4) 8250`

PV = $7052.13