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**Unformatted text preview: **0,105 + 14,396 = 154,501 21
21 Annuities on the Spreadsheet Annuities
Example
Example The present value and future value
The formulas in a spreadsheet include a
place for annuity payments
place Click on the Excel icon to see an
Click
example
example 22
22 Quick Quiz – Part II You know the payment amount for a loan and
You
you want to know how much was borrowed.
Do you compute a present value or a future
value?
value?
You want to receive 5,000 per month in
You
retirement. If you can earn .75% per month
and you expect to need the income for 25
years, how much do you need to have in your
account at retirement?
account 23
23 Finding the Payment Suppose you want to borrow $20,000 for a new
Suppose
car. You can borrow at 8% per year,
compounded monthly (8/12 = .66667% per
month). If you take a 4 year loan, what is your
monthly payment?
monthly 20,000 = C[1 – 1 / 1.006666748] / .0066667
C = 488.26 24
24 Finding the Payment on a
Finding
Spreadsheet
Spreadsheet Another TVM formula that can be found in a
Another
spreadsheet is the payment formula
spreadsheet PMT(rate,nper,pv,fv)
The same sign convention holds as for the PV and
The
FV formulas
FV Click on the Excel icon for an example 25
25 Finding the Number of Payments
Finding
– Example 6.6
Example Start with the equation and remember your
Start
logs.
logs. 1,000 = 20(1 – 1/1.015t) / .015
.75 = 1 – 1 / 1.015t
1 / 1.015t = .25
1 / .25 = 1.015t
t = lln(1/.25) / ln(1.015) = 93.111 months = 7.76
n(1/.25)
years
years And this is only if you don’t charge anything
And
more on the card!
more
26
26 Finding the Number of Payments
Finding
– Another Example
Another Suppose you borrow $2,000 at 5% and you are
Suppose
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 27
27 Finding the Rate Suppose you borrow $10,000 from your
Suppose
parents to buy a...

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