# Loan

• Feb 24th 2007, 10:10 AM
julie
Loan
James borrowed \$5,000 from his friend 2 years ago; and, an additional \$3,000 1 year ago. He wants to repay his friend the money that he borrowed plus interest at 8% compounded quarterly.

a) How much will James have to pay in 2 years time to fully repay his debt if he pays \$1,000 to-day & \$4,000 1 year from now?

b) Calculate James' payments if he wants to fully repay his debt with two equal payments - the first 9 months from now & the second 18 months from now.

Possible formula: Fv=PMT[ (1+i)^n -1 / i ]

• Feb 24th 2007, 09:52 PM
ticbol
Quote:

Originally Posted by julie
James borrowed \$5,000 from his friend 2 years ago; and, an additional \$3,000 1 year ago. He wants to repay his friend the money that he borrowed plus interest at 8% compounded quarterly.

a) How much will James have to pay in 2 years time to fully repay his debt if he pays \$1,000 to-day & \$4,000 1 year from now?

b) Calculate James' payments if he wants to fully repay his debt with two equal payments - the first 9 months from now & the second 18 months from now.

Possible formula: Fv=PMT[ (1+i)^n -1 / i ]

Let me use the formula for compound interest.
A = P(1 +i)^n --------------(1)
where
A = amount of investment after n numbers of compounding.
P = principal or initial value of investment
i = periodic rate, or relative rate per compounding
n = number of compoundings.

a)How much will James have to pay in 2 years time to fully repay his debt if he pays \$1,000 to-day & \$4,000 1 year from now?
Today:

Debt due to the \$5000 two years ago.
8% per annum compounding quarterly, so, i = 0.08/4 = 0.02
Two years ago, so, n = 2*4 = 8 compoundings.
A1 = 5000(1+0.02)^8 = \$5858.30 today.

Debt due to the \$3000 last year.
n = 1*4 = 4
A2 = 3000(1.02)^4 = \$3247.30

So, total debt today = A1 +A2 = 5856.30 +3247.30 = \$9105.60
Paying 1000 today,........ 9105.60 -1000 = \$8105.60 balance

------------
After 1 year from today.

P = 8105.60
i = 0.02
n = 1*4 = 4

New debt = 8105.60(1.02)^4 = \$8773.76
Paying 4000,........... 8773.76 -4000 = \$4773.76 new balance

-----------------------
For final payment two years from today.
That is 1 year from next year.

P = 4773.76
i = 0.02
n = 1*4 = 4

Newer debt = 4773.76(1.02)^4 = \$5167.27 ---------he's going to pay finally.

Therefore, James will have to pay the \$8000 he owed a total of (1000 +4000 +5167.27) = \$10,167.27 in two years from today. ------------answer.

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b) Use that formula?

Let me pass.
• Feb 25th 2007, 12:05 AM
ticbol
Quote:

Originally Posted by julie
James borrowed \$5,000 from his friend 2 years ago; and, an additional \$3,000 1 year ago. He wants to repay his friend the money that he borrowed plus interest at 8% compounded quarterly.

b) Calculate James' payments if he wants to fully repay his debt with two equal payments - the first 9 months from now & the second 18 months from now.

Possible formula: Fv=PMT[ (1+i)^n -1 / i ]

That formula is not applicable to the problem, I'm afraid.
Let me do it analytically.

Let us say N = amount of equal payments each.

After 9 months from today:
The \$5000 loan is [2 +(9/12)] = 2.75 years old, so, n1 = 2.75*4 = 11 compoundings
The \$3000 loan is 1.75 years old, so, n2 = 1.75*4 = 7 compoundings
So his total debt 9 months from now is
A(9) = 5000(1.02)^11 +3000(1.02)^7 = \$9662.93
Paying N,
Balance = 9662.93 -N -----------**

---------------------
After 18 months from today.
That is 9 months from 9 months from today. :)
So,
P = 9662.93 -N
i = 0.02
n = (9/12)*4 = 3 compoundings

New debt = (9662.93 -N)(1.02)^3
That is equal to N, for his second and last equal payment.
So,
(9662.93 -N)(1.02)^3 = N
We just isolate N and we're done.
9662.93 -N = N /(1.02^3)
9662.93 = N +[N /(1.02^3)]
9662.93 = N[1 +1/(1.02^3)]
9662.93 = N(1.942322335)
N = 9662.93 / 1.942322335 = 4974.94

Therefore, here, James has to pay \$4974.94 twice to fully pay his debts is 18 months. -----------answer.
• Feb 25th 2007, 06:13 AM
julie
thnx
Thank you so much, i was completley lost on this question even though it seems simple now. Again thanks!:)