If a principal P is borrowed at an annual rate r, then after t years if interest is compounded n times a year, the borrower will owe the lender an amount A given by nt A = P (1+)" In this case, r/n is the interest rate per compounding period and nt is the number of compounding periods. (a) Suppose that you borrow 100 USD, your interest rate is 6%. Based on the number of yearly compounds, how much will you owe after 2 years? To answer this, find A(n) then copy and complete the following table. Round to 4 decimal places in this HW. Compounding Frequency Annually Semiannually Quarterly Monthly Weekly A(n) 1 112.7160 52 365 Hourly 8760 (b) Describe, in words, what happens as n increases. (c) Now suppose n → 0. Go back to the original form of A (without the numbers from part a). What does A(n) approach? Your answer should depend on the other variables. Show all steps of the limit computation.
If a principal P is borrowed at an annual rate r, then after t years if interest is compounded n times a year, the borrower will owe the lender an amount A given by nt A = P (1+)" In this case, r/n is the interest rate per compounding period and nt is the number of compounding periods. (a) Suppose that you borrow 100 USD, your interest rate is 6%. Based on the number of yearly compounds, how much will you owe after 2 years? To answer this, find A(n) then copy and complete the following table. Round to 4 decimal places in this HW. Compounding Frequency Annually Semiannually Quarterly Monthly Weekly A(n) 1 112.7160 52 365 Hourly 8760 (b) Describe, in words, what happens as n increases. (c) Now suppose n → 0. Go back to the original form of A (without the numbers from part a). What does A(n) approach? Your answer should depend on the other variables. Show all steps of the limit computation.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:If a principal P is borrowed at an annual rate r, then after t years if interest is compounded
n times a year, the borrower will owe the lender an amount A given by
nt
= P (1 + )"
A =
In this case, r/n is the interest rate per compounding period and nt is the number of
compounding periods.
(a) Suppose that you borrow 100 USD, your interest rate is 6%. Based on the number of
yearly compounds, how much will you owe after 2 years? To answer this, find A(n)
then copy and complete the following table. Round to 4 decimal places in this HW.
A(n)
Compounding Frequency
Annually
Semiannually
Quarterly
Monthly
Weekly
n
1
112.7160
52
365
Hourly
8760
(b) Describe, in words, what happens as n increases.
(c) Now suppose n → 0. Go back to the original form of A (without the numbers from
part a). What does A(n) approach? Your answer should depend on the other variables.
Show all steps of the limit computation.
(d) The result is called the continuous compound interest formula. Using this function and
the values from part a), how much interest will you owe after 2 years?
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