Holooly Plus Logo
Holooly Plus Logo

Question 5.P.7: Calculate the factors [F/A, 7%, 20] and [A/G, 7%, 20] used i......

Calculate the factors [F/A, 7%, 20] and [A/G, 7%, 20] used in Problem 5.6.

Step-by-Step
The 'Blue Check Mark' means that this solution was answered by an expert.
Learn more on how do we answer questions.
Report Answer

By (5.4),

F/A  =  \frac{e^m  –  1}{e^r  –  1}    (5.4) \\\\ [F/A,  7\%,  20]  =  \frac{e^{(0.07)(20)}  –  1}{e^{0.07}  –  1}  –  \frac{4.055200  –  1}{1.072508  –  1}  =  42.1359

and, By (5.8),

A/G  =  \frac{1}{e^r  –  1}  –  \frac{n}{e^m  –  1}    (5.8) \\\\ [A/g,  7\%,  20]  =  \frac{1}{e^{0.07}  –  1}  –  \frac{20}{e^{(0.07)(20)}  –  1}  =  \frac{1}{1.072508  –  1}  –  \frac{20}{4.055200  –  1}  =  7.2454

Related Answered Questions

Question: 5.1

A savings bank is selling long-term savings certificates that pay interest at the rate of 7 1/2% per year, compounded continuously. The bank claims that the actual annual yield of these certificates is 7.79%. What does this mean? ...

Verified Answer:

The nominal interest rate is 7\frac{1}{2}[/...
Question: 5.2

A savings bank offers long-term savings certificates at 7 1/2% per year, compounded continuously. If a 10-year certificate costs $1000, what will be its value at maturity? Compare with the value that would be obtained if the interest were compounded annually rather than continuously. ...

Verified Answer:

From (5.2), F/P = e^m          (5.2...
Question: 5.3

A savings account earns interest at the rate of 6% per year, compounded continuously. How much money must initially be placed in the account to provide for twenty end-of-year withdrawals, if the first withdrawal is $1000 and each subsequent withdrawal increases by $200? ...

Verified Answer:

The solution may be formulated after (2.11): P = A...
Question: 5.6

At what rate must funds be continuously added to a savings account in order to accumulate $10 000 in 15 years, if interest is paid at 5% per year, compounded continuously? ...

Verified Answer:

By (5.10), \bar{A}/F  =  \frac{r}{e^m  -  1...
Question: 5.P.1

What effective annual interest rate corresponds to a nominal interest rate of 10% per year, compounded continuously? ...

Verified Answer:

i  =  e^{0.10}  -  1  =  0.105171  ≈  10.52...
Question: 5.P.6

Ms. Brown deposits $1000 in the bank at the end of the first year, $1200 at the end of the second year, etc., continuing to increase the amount by $200 a year, for 20 years. If the bank pays 7% per year, compounded continuously, how much money will have accumulated at the end of 20 years? ...

Verified Answer:

Writing A′ = $1000 + A, we have, from Section 2.7,...
Question: 5.P.8

Mrs. Carter deposits $100 in the bank at the end of each month. If the bank pays (a) 6% per year, (b) 7% per year, compounded continuously, how much money will she have accumulated at the end of 5 years? (Compare Problem 4.11.) ...

Verified Answer:

(a) The nominal monthly interest rate is 6%/12 = 0...
Question: 5.P.9

In Problem 5.8, suppose Mrs. Carter deposits $100 a month during the first year, $110 a month during the second year, $120 a month during the third year, etc. How much will have accumulated at the end of 5 years if the interest rate is 6% per year, compounded continuously? (Compare Problem 4.12.) ...

Verified Answer:

Proceeding as in Problem 4.12, we have: F = $100[F...
Question: 5.P.10

Suppose that $2000 is deposited each year, on a continuous basis, into a savings account that pays 6% per year, compounded continuously. How much money will have accumulated after 12 years? ...

Verified Answer:

With \bar{A} = $2000 per year, (5....
Question: 5.4

A person borrows $5000 for 3 years, to be repaid in 36 equal monthly installments. The interest rate is 10% per year, compounded continuously. How much money must be repaid at the end of each month? ...

Verified Answer:

Calculating [A/P, 10%, 12,36] by (5.6), we have [l...