Question

A hotel investment company is considering to add another hotel to its portfolio. The sales price is currently at $ 5,000,000. The purchase is partially financed by a loan with an LTV of 60%. The bank offers a 20-year monthly amortizing mortgage with a nominal interest rate of 6%. How much goes towards the principal in the second year?

a)      $ 52,061

b)      -$ 43,599

c)       $ 1,557,428

d)      $ 85,034

Answer 1

Using formula

Loan=60%*5000000=3000000.0000

Monthly payment=Loan*(rate/12)/(1-1/(1+rate/12)^(12*t))=3000000.0000*(6%/12)/(1-1/(1+6%/12)^(12*20))=21492.9318

Loan oustanding at the end of first year=Loan*(1+rate/12)^(12*1)-Monthly payment/(rate/12)*((1+rate/12)^(12*1)-1)=3000000.0000*(1+6%/12)^(12*1)-21492.9318/(6%/12)*((1+6%/12)^(12*1)-1)=2919906.0348

Loan outstanding at the end of second year=Loan*(1+rate/12)^(12*2)-Monthly payment/(rate/12)*((1+rate/12)^(12*2)-1)=3000000.0000*(1+6%/12)^(12*2)-21492.9318/(6%/12)*((1+6%/12)^(12*2)-1)=2834872.0491

Principal paid during second year=2919906.0348-2834872.0491=85033.9857

Using Excel

=FV(6%/12,12*1,PMT(6%/12,12*20,-60%*5000000),-60%*5000000)-FV(6%/12,12*2,PMT(6%/12,12*20,-60%*5000000),-60%*5000000)

=85033.9857