Question

Using technology, determine the present value given that you make semi-annual payments of $2,527 at 6.1% compouded semi-annually over a 6 year period. Round your answer to the nearest cent.

Answer 1

PVAO=2527[(1-(1+0.061/2)^(-2*6))/(0.061/2)=25078.86

Answer 2

The present value is $21070.31

Explanation:

Given: semi-annual payments of $2,527 at 6.1% compounded semi-annually over a 6 year period.

We have to find the present value given that semi-annual payments of $2,527 at 6.1% compounded semi-annually over a 6 year period.

Given that payment is made semi annually that is 2 times in a year.

Given Payment made = $2527.

Rate of interest =6.1% compounded semi annually = 0.061

Time period = 6 years = 6 × 2 = 12

Thus,
`P=(A\cdot i)/(1-(1+i)^(-t))`

Where A denotes the amount to pay

P is payment made

t is time period

i is interest rate

Substitute the values, we get,

`2527=(A\cdot(0.061) )/(1-(1+0.061)^(-12))`

Cross multiply and Solve for A, we get,

`A=2527\cdot(\left(1-\left(1+0.061\right)^(-12)\right))/(0.061)`

A=21070.306476

Thus, the present value is $21070.31