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Unformatted text preview: 0,105 + 14,396 = 154,501 21
21 Annuities on the Spreadsheet Annuities
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
22 Quick Quiz – Part II You know the payment amount for a loan and
you want to know how much was borrowed.
Do you compute a present value or a future
You want to receive 5,000 per month in
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?
23 Finding the Payment Suppose you want to borrow $20,000 for a new
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 20,000 = C[1 – 1 / 1.006666748] / .0066667
C = 488.26 24
24 Finding the Payment on a
Spreadsheet Another TVM formula that can be found in a
spreadsheet is the payment formula
The same sign convention holds as for the PV and
FV Click on the Excel icon for an example 25
25 Finding the Number of Payments
– Example 6.6
Example Start with the equation and remember your
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
years And this is only if you don’t charge anything
more on the card!
26 Finding the Number of Payments
– Another 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 27
27 Finding the Rate Suppose you borrow $10,000 from your
parents to buy a...
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