[SPLIT, MOVED] compound interest, annuities, etc

[manching]

I am working on my business math, and have these questions:

1) i if borrow for 15 years the interest rate is 8% compounded annually and i am able to make the following repayments per year?

a. @12000
b. $15000
c. $18000

i have no idea how to make up this one please help me.

2) a loan of $120,000 is taken out over a 20-year period and interest is charged at 7.5% per annum. find the amount of each repayment if the loan is compounded:

i. annually
ii 6-monthly
iii quarterly

Please help. Many thanks!

manching

 

[stapel]

1) I don't see that any actual question has been posed here. You are borrowing some amount (unstated) and making various different payments over the years. But so what? What are you supposed to do with this information?

2) Use the compound-interest formula they gave you.

Eliz.

 

[soroban]

Hello, manching!

Two questions . . .

(1) If you are given an Amorization problem,
. . how come you were not given the Amortization Formula?

(2) Are the payments made at each compounding period?

2) A loan of $120,000 is taken out over a 20-year period
and interest is charged at 7.5% per annum.
Find the amount of each repayment if the loan is compounded:

(a) annually
(b) semiannually
(c) quarterly

Amortization Formula: \(\displaystyle \L\:A \;=\;P\frac{i(1\,+\,i)^n}{(1\,+\,i)^n\,-\,1}\)

. . where: \(\displaystyle \:\begin{array}{ccc}P & = & \text{principal borrowed} \\ i & = &\text{periodic interest rate} \\ n & = & \text{number of periods} \\ A & = & \text{periodic payment}\end{array}\)


(a) annual: \(\displaystyle \\,=\,120,000.\;i\,=\,0.075,\;n\,=\,20\)

\(\displaystyle \L A\;=\;120,000\frac{(0.075)(1.075)^{20}}{(1.075)^{20}\,-\,1} \;\approx\; \$11,771.06\)


(b)semmiannual: \(\displaystyle \\,=\,120,000,\;i\,=\,\frac{7.5\%}{2} \,=\,0.0375,\;n\,=\,40\)

\(\displaystyle \L A\;=\;120,000\frac{(0.0375)(1.0375)^{40}}{(1.0375)^{40}\,-\,1} \;\approx\;\$5839.13\)


(c) quarterly: \(\displaystyle \\,=\,120,000,\;i \,=\,\frac{7.5\%}{4} \,=\,0.01875,\;n\,=\,80\)

\(\displaystyle \L A \;=\;120,000\frac{(0.01875)(1.01875)^{80}}{(1.01875)^{80}\,-\,1} \;\approx\;\$2907.92\)

 

[Denis]

1) i if borrow for 15 years the interest rate is 8% compounded annually and i am able to make the following repayments per year?
a. $12000
b. $15000
c. $18000

Looks like you want to calculate the amount you can borrow;
formula: A = P(1 + f) / i where f = 1 / (1 + i)^n

1st case: A = 12000(1 + f) / .08 where f = 1 / (1.08)^15

 

[manching]

Denis,

many thanks to solve the questions I was posting , you made my day.


have a lovely day

manching

 

[manching]

Soroban,

Many thanks to solve the questions I posted, you made my day.



Discounted interest rate count: the questionis?

Formul : Amount borrowed= 100xsum required (divided) 100-(discount interest ratexlength of the loan in years) that for started loan which it pay up front interest plus principal.

100x3000 divided 100-(0.075x12months) and according to this formula ask me to culculate equivalent flat and simple interest rated for the following loan I will borrow?

I borrow 3000 from bank and the discounted interest rate is 7.5% the loan for 12 months?

regards

manching