Sinking fund question

[BrainMan]

I have this question I can't figure out:

$1000 is borrowed for 20 years at 5% effective. The borrower does not pay interest currently and will pay all accrued interest at the end of 20 years together with the principal. (a) Find the total annual sinking fund deposit necessary to liquidate the loan at the end of 20 years if the sinking fund earns 4% effective. (b) Find the total annual amortization payment at 5% effective.

The annual interest payment will obviously be (1000)(.05) = 50.
These payments will accumulate according to an annuity-immediate with time = 20 and i = .05. Thus, these accumulate to (50)[((1.05)^20) - 1)/.05) = 1653.30. I just don't see what I do now.

I'm in a university-level first-year interest class and I'm studying for an exam. Would someone mind showing me how to do this problem? I have more done, but it's tough to show on the computer. I understand all the formulas, so any help doesn't have to be completely worked out.

Thanks in advance.
Tim

[songjiong]

I have this question I can't figure out:

$1000 is borrowed for 20 years at 5% effective. The borrower does not pay interest currently and will pay all accrued interest at the end of 20 years together with the principal. (a) Find the total annual sinking fund deposit necessary to liquidate the loan at the end of 20 years if the sinking fund earns 4% effective. (b) Find the total annual amortization payment at 5% effective.

The annual interest payment will obviously be (1000)(.05) = 50.
These payments will accumulate according to an annuity-immediate with time = 20 and i = .05. Thus, these accumulate to (50)[((1.05)^20) - 1)/.05) = 1653.30. I just don't see what I do now.

I'm in a university-level first-year interest class and I'm studying for an exam. Would someone mind showing me how to do this problem? I have more done, but it's tough to show on the computer. I understand all the formulas, so any help doesn't have to be completely worked out.

Thanks in advance.
Tim

This is my solution:
a) SFP [1.04^20-1]/0.04 = 1000 SFP=33.58

b) 1000 = PMT [1-1.05^(-20)]/.05 PMT= 80.24

total annual amortization payment =20* 80.24= 1604.8

Do I get the right answer?

[BrainMan]

I don't have the solutions (even number in my text). Can anyone corroborate this?

Thanks for helping me.

[songjiong]

Sinking fund is another method to repay loan. Under this method,we treat the principal and interest separately. The interest is paid annually or in a lump sum at maturity date. The principal should be offset by the SFP accumulated value at maturity, since interest will be paid separately, the principal will keep unchanged till maturity.

This is my comprehnsion about sinking fund. I take great trouble to fully understand the real meaning. If you get this, most SFP problems will not be difficult.

[BrainMan]

How does the fact that he doesn't pay the interest until the end play into the problem?

[songjiong]

1,000* (1.05^20) = SFP [(1.04^20 -1)/.04]

SFP= 89.10

If singking fund is also 5%, then SFP will be the same as amortization payment.

Is this the right solution?

[BrainMan]

Can anyone confirm this? Somehow I think it's more complicated than that. The fact that the interest doesn't get paid til the end makes it more involved than what you wrote I believe.

[wonderacle]

for a), the wording is a little bit confusing for me,
but i think what it asks for is the annual deposit,
since the interest is 50, like what you say,
and it is increasing and accrued on a yearly basis,
the total payment at t20 is
1000+50(Is angel 20) @ 5%,
this should equal to the sinking fund amount at t20, i.e.
X s angel 20@ 4%,
solve the equation will give you the result,

I am not sure what b) is asking for, so sorry for that,

[zmkramer]

I have this question I can't figure out:

$1000 is borrowed for 20 years at 5% effective. The borrower does not pay interest currently and will pay all accrued interest at the end of 20 years together with the principal. (a) Find the total annual sinking fund deposit necessary to liquidate the loan at the end of 20 years if the sinking fund earns 4% effective. (b) Find the total annual amortization payment at 5% effective.

The annual interest payment will obviously be (1000)(.05) = 50.
These payments will accumulate according to an annuity-immediate with time = 20 and i = .05. Thus, these accumulate to (50)[((1.05)^20) - 1)/.05) = 1653.30. I just don't see what I do now.

I'm in a university-level first-year interest class and I'm studying for an exam. Would someone mind showing me how to do this problem? I have more done, but it's tough to show on the computer. I understand all the formulas, so any help doesn't have to be completely worked out.

Thanks in advance.
Tim

I did not read any of the previous posts but here is how you do the problem. If i borrow X at interest i and intend to pay at time T (in years) the principal plus accrued interest i would pay X(1+i)^T.

You want to deposit money into a sinking fund that accrues to the amount of money you owe, the principal. Well in this case you want it to accrue to the principal plus interest.

So if its 1000(1.05)^20 = SFP *s [20 @ 4%]

SFP = 89.10238108 (i didn't feel like rounding)

If you were just paying regular loan payments based on 5% interest they would be

LP = 80.24258719

[natalielphie]

Is there a way to calculate the loan amount when you are given nonlevel amounts for sinking fund payments? I know how to use the formula for solving with level payments, L=K(((1+j)^n-1)/(j))/(1+i((1+j)^n-1)/(j)), where j is the rate of the sinking fund, and i is the yield rate earned on the loan. I don't know if there is a general formula for nonlevel payments of K, but one would definitely be useful! If needed, I can give the exact problem, but this is the jist of it.
Thanks.