This summary contains all compulsory literature and all transcribed lectures of the course Real Estate Investment (REI). This document contains everything for you to pass the exam!
,Week 01 – Residential mortgages
Ch. 3
Financing the purchase of real estate usually involves borrowing on a long- or short-term basis.
Because large amounts are usually borrowed in relation to the prices paid for real estate, financing
costs are usually significant in amount and weigh heavily in the decision to buy property.
Future value
Compounding
Compounding = to future values with a nominal annual rate → FV = PV * (1+r) ^ n
➔ 10.000 * (1 + 6%) = $10.600
Compounding intervals (monthly, quarterly and semi-annual) → FV = PV * (1+(r/n)^n*m
1. 0.06/12 = 0.005
2. 10000*(1+0.005)^12 = 10.616,78
Therefore, you can see that monthly compounding has benefits because you have more at the end of
the year with annual compounding.
Another way of looking at this;
Computing the Effective Annual Yield (EAY) → new (FV) – old (PV) / old (PV)
➔ Compounded monthly = $10.616,78 - $10.000,00 / $10.000,00 = 6.1678%
➔ Compounded annually = $10.600,00 - $10.000,00 / $10.000,00 = 6%
From this comparison we can conclude that the EAY is higher when monthly compounding is used.
In our example, we could say that a 6 percent annual rate of interest compounded monthly provides
an effective annual yield of 6.168 percent.
Many banks disclose what is referred to as the Annual Percentage Yield (APY). Conceptually this is
the same as the EAY. However, the EAY may differ from the APY. Subsequently, the APY won’t be
considered in calculations in this book.
Calculating compound interest factors
Finding a solution to a compounding problem involving many periods is very awkward because of the
amount of multiplication required. A way to solve this can be done by calculating interest factors.
With the previous example ($10,000 deposit at a nominal rate of 6%), the corresponding interest
factor for one year would be;
➔ $10,000 *(1,060000) = $10,600
You can determine the interest factors in excel, using; FV(PV;RATE;N;PMT), where
- PV = $1
- Rate = 6%
- Nper = 1
- PMT = 0
➔ Solve for FV = 1.06
Or, if we wanted the factor for 10% interest and four years, we would have a FV of;
- PV = $1
- Rate = 10%
- N=4
- PMT = 0
➔ Solve for FV = 1.464100
By calculating the annual interest factor, we can now determine the future value of $5.000;
➔ $5.000 *(1.464100) = $7,230.50
Calculating a compound interest factor with monthly compounding goes as follows;
➔ (1+0.06/12)^12 = 1.061678
, Therefore, what is the FV of $5,000, with 8% interest and monthly compounding at N = 2;
➔ $5,000 * (1+0.08/12)^24 = $5,564.44
Future values in excel
FV(Rate;PMT;PV;N)
Annual compounding;
- N=1
- R = 6%
- PMT = 0
- PV = -$10,000
- Solve FV in excel = $10,600
Question; What is the future value of $5,000 deposited for four years compounded at an annual rate
of 10 percent?
- N=4
- Rate = 10%
- PMT = 0
- PV = -$5,000
- FV = $7,320.50
Question: What is the future value of a single $5,000 deposit earning 8 percent interest,
compounded monthly, at the end of two years?
- N = 24 (2 years * 12 months)
- Rate = 0.666% (8%/12)
- PMT = 0
- PV = -$5,000
- FV = $5,864.44
Present value
Discounting = FV / (1+ R)^N
Present value interest factors
Calculating interest factors in excel (function n, rate, PMT, FV);
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