Question

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

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