Compound Interest Question: Dave and his sock-drawer plan

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KarlyD

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Dave has a student loan of $10 000 on January 1, 2000. The loan has an interest rate of 9% per annum, compounded monthly. Instead of paying off the loan, Dave places a bundle of money in his sock drawer. He puts away an equal amount of money each month. Over the next 5 years, Dave receives several notices from the bank, demanding that he make his payments, but he ignores them. After 5 years, Dave removes all the money from his sock drawer and pays off the entire loan in one massive payment before the bank hauls him off to jail.

a) The bank recommends that Dave pay the bank $207.59 a month to pay off the loan in 5 years. How much money does Dave lose each month by adopting his sock drawer plan?

b) If the bank compounds the interest every two months instead of every month, how much money must Dave pay?

Would someone mind explaining how to go about this question? I'm starting from scratch with part A. Any guidance would be greatly appreciated. Thanks a lot! :)
 
Re: Compound Interest Question

KarlyD said:
Dave has a student loan of $10 000 on January 1, 2000. The loan has an interest rate of 9% per annum, compounded monthly. Instead of paying off the loan, Dave places a bundle of money in his sock drawer. He puts away an equal amount of money each month. Over the next 5 years, Dave receives several notices from the bank, demanding that he make his payments, but he ignores them. After 5 years, Dave removes all the money from his sock drawer and pays off the entire loan in one massive payment before the bank hauls him off to jail.

a) The bank recommends that Dave pay the bank $207.59 a month to pay off the loan in 5 years. How much money does Dave lose each month by adopting his sock drawer plan?

b) If the bank compounds the interest every two months instead of every month, how much money must Dave pay?

Would someone mind explaining how to go about this question? I'm starting from scratch with part A. Any guidance would be greatly appreciated. Thanks a lot! :)
Click to expand...

You had it posted before:

http://www.freemathhelp.com/forum/viewt ... ght=#97936

Why are you starting from scratch - what part is confusing in your solution?
 
Re: Compound Interest Question

KarlyD said:
Dave has a student loan of $10 000 on January 1, 2000. The loan has an interest rate of 9% per annum, compounded monthly. Instead of paying off the loan, Dave places a bundle of money in his sock drawer. He puts away an equal amount of money each month. Over the next 5 years, Dave receives several notices from the bank, demanding that he make his payments, but he ignores them. After 5 years, Dave removes all the money from his sock drawer and pays off the entire loan in one massive payment before the bank hauls him off to jail.

a) The bank recommends that Dave pay the bank $207.59 a month to pay off the loan in 5 years. How much money does Dave lose each month by adopting his sock drawer plan?
Click to expand...
I am assuming that you are seeking the net loss out of his pocket by adpting the sock drawer approach as opposed to paying the $207.59 determined by the bank.

If he allows the initial loan amount of $10,000 to accumulate interest over 60 months, it will result in an amount of S = P(1 + i)^n = 10,000(1 + .0075)^60 = $15,657 owed at the end of 5 years.

If he paid off the loan at the bank's required monthly payment, his interest for the first month would be .0075(10,000) = $75.00.

His interest for the last payment would be 205.59 - 207.59/1.0075 = $1.54.

The total loan interest over the 60 months would be 207.59(60) - 10,000 = $2455.

His interest would steadily decrease from $75.00 to $1.54 over the 60 months being considered with an average being $2455/60 = $40.92.

His net, out of pocket, monthly loss would be $5657 - 2455 = 3202/60 = $53.36 per month.

In summary, if he left the loan unpaid for 60 months, he would owe the bank $15,657.
Had he paid the bank's monthly payment of $207.59, he would have paid out $12,455.
The sock drawer gambit therefore cost him $3202 more at an averag monthly loss of $53.36.

I hope this what you were looking for.
 
Thanks a lot for the help!

I'm a little confused at how you got 205.59 here:

His interest for the last payment would be 205.59 - 207.59/1.0075 = $1.54.
 
Thanks a lot for the help!

I'm a little confused at how you got 205.59 here:

His interest for the last payment would be 205.59 - 207.59/1.0075 = $1.54.

Each payment is comprised of the outstanding balance on the principal plus the interest due on that principal due.

The final payment is therefore P + (.09/12)P or 1.0075P

Having the payment of $207.59, working backwards, the starting principal for the last month is 207.59/1.0075 = $205.59/1.0075 = $206.04. The interest due on $206.04 is then 206.05(.0075 = $1.54 for a total due of $207.59.

I see where I must have pushed the wrong key or somethng as the "205.59 - 207.59/1.0075 = $1.54" should read "207.59 - 207.59/1.0075 = 207.59 - 1.54 = $206.04", the interest still being $1.54.
 
Karly, that can be done quite simply:

has to pay 10000(1.0075)^60 = 15,656.81

would have paid 60 * 207.59 = 12,455.40

Difference = 3,201.41

On part b) :
b) If the bank compounds the interest every two months instead of every month, how much money must Dave pay?

10000(1 + .09/6)^30 = 10000(1.015)^30 = 15,630.80
 
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