Math Is Fun Forum

Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

Ask About Annuity

Mr. Budi borrows 2,000,000IDR which will be amortized with 10 annuities. The first annuity will be paid in 1 year with 10% per year interest. Make the installment plan!
For the annuity I got A =

=

=

=

=

(

is a geometric sequence with the first term

and ratio

)
=

=

= 2,000,000 × 0.61445671 = 1,228,913.42
Thus, the annuity is 1,228,913.42.
On the end of first year:
Annuity = 1,228,913.42IDR
Interest : 10% × 2,000,000IDR = 200,000IDR
Installment : 1,228,913.42IDR – 200.000IDR = 1,028,913.42IDR
Remaining loan : 2,000,000IDR – 1,028,913.42IDR = 971,086.58IDR
On the end of second year:
Annuity = 1,228,913.42IDR
Interest : 10% × 971,086.58IDR = 97,108.66IDR
Installment : 1,228,913.42IDR – 97,108.66IDR = 1,131,804.76IDR
Remaining loan    : 971,086.58IDR – 1,131,804.76IDR = -159.718,58IDR
Why am I seeing negatives already?

Last edited by Monox D. I-Fly (2018-05-15 21:40:24)

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Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

Re: Ask About Annuity

hi Monox D. I-Fly

I notice no one has answered this yet.  Maybe this post will 'bump it' to someone's attention.  In case not:

I don't know about using annuities for borrowing purposes so I cannot at the moment understand what you are doing here.  But it's still possible we can work together to a solution.  I have done this in the past.  The poster explains more about what they are doing and then I can understand enough to make a contribution.  Together we may get there

Here's what I do understand.

(1) If you borrow money you have to pay it back with interest. I cannot see what the rate for this would be in your question.

(2) If you invest money (usually for retirement) in an annuity, you pay regular amounts and the value accumulates because of this and interest earned. (at 10% ??)

(3) You want the ten year annuity value to  be equal to the ten year amount owed for the loan so it can be paid off.

Please let me know if I'm correct so far.

Bob

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