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Unformatted text preview: Example
Another Suppose you borrow $2,000 at 5% and you are
going to make annual payments of $734.42.
How long before you pay off the loan?
How 2,000 = 734.42(1 – 1/1.05t) / .05
.136161869 = 1 – 1/1.05t
1/1.05t = .863838131
1.157624287 = 1.05t
t = ln(1.157624287) / ln(1.05) = 3 years 29 Finding the Rate Suppose you borrow $10,000 from your
parents to buy a car. You agree to pay
$207.58 per month for 60 months. What is the
monthly interest rate?
monthly Sign convention matters!!!
CPT I/Y = .75% 30 Annuity – Finding the Rate
Without a Financial Calculator
Without Trial and Error Process Choose an interest rate and compute the PV of the
payments based on this rate
Compare the computed PV with the actual loan amount
If the computed PV > loan amount, then the interest rate
is too low
If the computed PV < loan amount, then the interest rate
is too high
Adjust the rate and repeat the process until the computed
PV and the loan amount are equal
PV 31 Quick Quiz – Part III You want to receive $5,000 per month for the next 5
years. How much would you need to deposit today if
you can earn .75% per month?
What monthly rate would you need to earn if you only
have $200,000 to deposit?
Suppose you have $200,000 to deposit and can earn .
75% per month. How many months could you receive the $5,000
How much could you receive every month for 5 years? 32 Future Values for Annuities Suppose you begin saving for your
Suppose retirement by depositing $2,000 per year
in an IRA. If the interest rate is 7.5%, how
much will you have in 40 years?
much FV = 2,000(1.07540 – 1)/.075 = 454,513.04 33 Annuity Due You are saving for a new house and you
You put $10,000 per year in an account paying
8%. The first payment is made today.
How much will you have at the end of 3
years? FV = 10,000[(1.083 – 1) / .08](1.08) =
35,061.12 34 Annuity Due Timeline
0 10000 1 10000 2 3 10000
35 Perpetuity – Example 6.7 Perpetuity formula: PV = C / r Current required return: 40 = 1 / r
r = .025 or 2.5% per quarter Dividend for new preferred: 100 = C / .025
C = 2.50 per quarter 36 Quick Quiz – Part IV You want to have $1 million to use for
retirement in 35 years. If you can earn 1% per
month, how much do you need to deposit on a
monthly basis if the first payment is made in
What if the first payment is made today?
You are considering preferred stock that pays a
quarterly dividend of $1.50. If your desired
return is 3% per quarter, how much would you
be willing to pay?
37 Work the Web Example Another online financial calculator can be found
Click on the web surfer and work the following
example Choose calculator and then annuity
You just inherited $5 million. If you can earn 6% on
your money, how much can you withdraw each year
for the next 40 yea...
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