FINA 210 – Introduction to Real Estate
Professor Masters
Leverage Exercises – THE SOLUTIONS
1. Calculate the monthly payments on a $100,000 loan with an 10% interest rate and a 20-year
amortization.
$965.03 (PV=100000, N=20*12=240, FV=0, I/Y=10/12=.833333, P/Y=1, C/Y=1, CPT PMT=965.03)
2. Calculate the annual interest rate on a $250,000 loan requiring 25 years to fully amortize with
monthly payments of $2,633.06.
1% *12=12% (PV=250000, N=25*12=300, PMT=-2633.06, FV=0, P/Y=1, C/Y=1, CPT I/Y=1)
3. Calculate the amortization period of a $500,000 loan, with an annual interest rate of 18%
requiring monthly payments of $7,716.56.
240/12=20 years (PV=500,000, PMT=-7716.56, I=18/12=1.5, FV=0, P/Y=1, C/Y=1, CPT N=240)
4. Calculate the balloon payment after 5 years on a $100,000 loan with an 10% interest rate, a 20year amortization and monthly payments of $965.02
FV=89,802.44 (PV=100000, I/Y=10/12=.83333, N=5*12=60, PMT=-965.02, P/Y=1, C/Y=1, CPT
FV=-89802.57)
5. Calculate the balloon payment after 10 years on a $1,000,000 loan with an 12% interest rate, a
25-year amortization and monthly payments of $10,532.24
FV=877,564.21 (PV=1000000, I/Y=12/12=1, N=10*12=120, PMT=-10532.24, P/Y=1, C/Y=1, CPT
FV=-877564.21)
6. Calculate the monthly payments for a $1,000,000 mortgage with a 10% interest rate and a 25year amortization.
$8,944.87 (P/Y=12, C/Y=2, I/Y=10, N=25*12=300, PV=1000000, FV=0, CPT PMT=-8944.87)
7. Calculate the monthly payments for a $500,000 mortgage with a 12% interest rate and a 20-year
amortization.
$5,404.87 (P/Y=12, C/Y=2, I/Y=12, N=20*12=240, PV=500000, FV=0, CPT PMT=-5404.87)
8. Calculate the monthly payments for a $750,000 mortgage with a 9% interest rate and a 15-year
amortization.
$7533.89 (P/Y=12, C/Y=2, I/Y=9, N=15*12=180, PV=750000, FV=0, CPT PMT=-7533.89)
9. Your building has been appraised at $2,000,000 using a cap rate of 12%. The lender is willing to
provide you a $1,500,000 mortgage loan with an amortization period of 25 years and a
mortgage interest rate of 12%. Calculate LTV of the loan, the monthly loan payments that you
must make and the DSCR.
LTV=1,500,000/2,000,000 = 75%
PMT $715,478.49 (P/Y=12, C/Y=2, I/Y=12, N=300, PV=1500000, FV=0, CPT PMT=-15478.49)
NOI=2000000*.12=240,000
DSCR=240000/(12*15478.49)=1.29
10. A building which generates an NOI of $500,000 has a capitalization rate of 8%. The lender offers
a mortgage loan of $2,750,000 with a 20-year amortization at an interest rate of 10%. Calculate
the Loan to Value (LTV) and the Debt Service Coverage (DSCR).
Building value=500,000/.08=$6,250,000
LTV=2,750,000/6,250,000=44%
PMT= $26,170.77 (P/Y=12, C/Y=2, I/Y=10, N=240, PV=2750000, FV=0, CPT PMT=-26170.77)
DSCR=500000 / (12*26170.77) = 1.59
11. What are the monthly payments on a $1,000,000 corporate loan to a real estate company if the
amortization period is 5 years and the interest rate is 12%?
$22,244.44 (P/Y=1, C/Y=1, I/Y=12/12=1, N=5*12=60, PV=1000000, FV=0, CPT PMT=-22244.44)
12. What is the yearly interest rate on a $500,000 corporate loan with an amortization of 8 years
and payments of 7,068.34?
I/Y=0.66666*12=8% (P/Y=1, C/Y=1, N=8*12=96, PV=500000, FV=0, PMT=-7068.34, CPT I/Y=0.66)
13. Your client is contemplating buying an industrial building for $1,000,000. He estimates that the
NOI for the first year will be $120,000. A lender has offered him a corporate loan of $500,000 at
a yearly interest rate of 8% with a 10 amortization. What is the DSCR of the loan.
PMT=$6,066.37 (P/Y=1, C/Y=1, I/Y=8/12=.666, N=120, PV=500000, FV=0, CPT PMT=-6066.37)
DSCR=120000 / (12*6066.37)=1.65
14. A building which generates an NOI of $700,000 has a capitalization rate of 10%. The lender
offers a mortgage loan of $3,750,000 with a 25-year amortization at an interest rate of 11%.
Calculate the Loan to Value (LTV) and the Debt Service Coverage (DSCR).
Building value=700000/.1=7,000,000
LTV=3750000/7000000=54%
PMT= $36,094.84 (P/Y=12, C/Y=2, I/Y=11, N=300, PV=3750000, FV=0, CPT PMT=-36094.84)
DSCR=700000 / (12*36094.84) = 1.62
15. Calculate the mortgage balance after 10 years if the initial mortgage is $1,500,000, with an
interest rate of 12% and a 20-year amortization.
PMT=16,214.62 (P/Y=12, C/Y=2, I/Y=12, N=240, PV=1500000, FV=0, CPT PMT=-16214.62)
FV (balance)=1,143,463.06 (P/Y=12, C/Y=2, I/Y=12, N=120, PV=1500000, PMT=-16214.62, CPT
FV=1143463.06)
16. Calculate the mortgage balance after 5 years if the initial mortgage is $1,000,000, with an
interest rate of 10% and a 25-year amortization.
PMT=8,944.83 (P/Y=12, C/Y=2, I/Y=10, N=300, PV=1000000, FV=0, CPT PMT=-8944.83)
FV (balance)=939,918.26 (P/Y=12, C/Y=2, I/Y=10, N=60, PV=1000000, PMT=-8944.83, CPT
FV=939918.26)