Cromwell is acquiring some land for $1200000 in exchange for semi annual payments of $75000 at an interest rate of 6.35%. how many years will it take cromwell to pay for this purchase

Question

Mathematics

Hana Graves

28 October, 22:11

Cromwell is acquiring some land for $1200000 in exchange for semi annual payments of $75000 at an interest rate of 6.35%. how many years will it take cromwell to pay for this purchase

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Averie Gutierrez · Answer 1

The formula of the present value of annuity ordinary is

Pv=pmt [ (1 - (1+r/k) ^ (-kn)) : (r/k) ]

Pv present value 1200000

PMT semiannual payment 75000

R interest rate 0.0635

K compounded semiannual 2

N time?

1200000=75000[ (1 - (1+0.0635/2) ^ (-2n)) : (0.0635/2) ]

Solve for n

1,200,000:75,000=[ (1 - (1+0.0635/2) ^ (-2n)) : (0.0635/2) ]

16=[ (1 - (1+0.0635/2) ^ (-2n)) : (0.0635/2) ]

16 * (0.0635:2) = (1 - (1+0.0635/2) ^ (-2n))

0.508 = (1 - (1+0.0635/2) ^ (-2n))

0.508-1 = - (1+0.0635/2) ^ (-2n)

-0.492 = - (1+0.0635/2) ^ (-2n)

0.492 = (1+0.0635/2) ^ (-2n)

-2n=log (0.492) : log (1+0.0635:2)

N=-[log (0.492) : log (1+0.0635:2) ]:2

N=11.35 years