# Problems Calcuating Interest (Time value of money)

• Sep 12th 2012, 03:07 PM
jegues
Problems Calcuating Interest (Time value of money)
I have concerns regarding questions attached.

2.13 - Can someone verify my results, am I doing this question correctly? (See 2nd attachment)

2.17 - I'm not sure how to do this one, I think I understand what I need to do in my head I'm just having trouble working out the math.

Firstly, what do they mean by effective interest rate? Is it still compounded monthly?

Here is my attempt at the single payment option:

$F = 3000*(1+0.12) = 3360$

Is this correct?

I'm not sure how to deal with the 12 payments as opposed to one single payment at the end. If we assumed one single payment at the end it would be as follows,

$F = 3000(1+0.12)^{12}$

How do I deal with 12 equal payments effectively decreasing the balance on which compounding interest is collected each month?

Thanks again!
• Sep 12th 2012, 03:54 PM
MaxJasper
Re: Problems Calcuating Interest (Time value of money)
#2.13 (a) :: 19.56%
#2.13 (b) :: \$1307.34-\$1000=\$307.34

#2.17 :: \$266.55*12-\$265.6*12=\$17.16

NB.: Might contain my own discounts!
• Sep 12th 2012, 05:41 PM
jegues
Re: Problems Calcuating Interest (Time value of money)
Quote:

Originally Posted by MaxJasper
#2.13 (a) :: 19.56%
#2.13 (b) :: \$1307.34-\$1000=\$307.34

#2.17 :: \$266.55*12-\$265.6*12=\$17.16

NB.: Might contain my own discounts!

Could you explain how you obtained those numbers for 2.17, I am still quite confused.

It's not obvious to me how you came up with \$266.55*12-\$265.6*12. What formula is that? How did you obtain the values 266.55 & 265.6?

Thank you!
• Sep 12th 2012, 08:29 PM
Wilmer
Re: Problems Calcuating Interest (Time value of money)
2.13:
307.34 is correct
For effective rate, you only need to do this: 1.015^12 - 1 = 1.195618... - 1 = .195618 ; so ~19.56%

2.17 :
required monthly payment = 266.55 ; 266.55 * 12 = 3198.60
single payment 1 year later at 12% effective: 3360.00 (which you have correctly)
3360.00 - 3198.60 = 161.40 = interest saved

Calculation of the monthly payment:
3000 * .01 / (1 - 1/1.01^12) = 266.54636....
• Sep 13th 2012, 08:55 AM
jegues
Re: Problems Calcuating Interest (Time value of money)
Quote:

Originally Posted by Wilmer
2.13:
307.34 is correct
For effective rate, you only need to do this: 1.015^12 - 1 = 1.195618... - 1 = .195618 ; so ~19.56%

2.17 :
required monthly payment = 266.55 ; 266.55 * 12 = 3198.60
single payment 1 year later at 12% effective: 3360.00 (which you have correctly)
3360.00 - 3198.60 = 161.40 = interest saved

Calculation of the monthly payment:
3000 * .01 / (1 - 1/1.01^12) = 266.54636....

Thank you that is much more clear.

Could you express the formula for monthly payment in terms of variables for me so I know what every number within that expression is?

Thanks again!
• Sep 13th 2012, 10:01 AM
Wilmer
Re: Problems Calcuating Interest (Time value of money)
Quote:

Originally Posted by jegues
Could you express the formula for monthly payment in terms of variables for me so I know what every number within that expression is?

P = payment (?)
A = amount of loan (3000)
n = number of payments (12)
i = interest per month (.01)

P = Ai / ( 1 - 1/(1 + i)^n)
• Sep 23rd 2012, 09:58 AM
jegues
Re: Problems Calcuating Interest (Time value of money)
Quote:

Originally Posted by Wilmer
2.17 :
required monthly payment = 266.55 ; 266.55 * 12 = 3198.60
single payment 1 year later at 12% effective: 3360.00 (which you have correctly)
3360.00 - 3198.60 = 161.40 = interest saved

I have a question here.

Why is it that here we can simply do the payment amount times the number of payments? (i.e. 266.55*12)

Aren't we ignoring the time value of money when we do this?

Shouldn't we be finding the future value given a payment amount? Or is the time value of money implied when we first calculated the payment amount? (i.e. \$266.55)

In this example,

For Q2), we first calculated the payment amount given a present value (that would be our \$266.55 in this question), and then to find out how much we paid given N peroids we calculated the future value given the payment amount for N peroids.

Which is the way is the correct way to do this?

Can you clarify Wilmer? Thanks again!
• Sep 23rd 2012, 10:13 AM
Wilmer
Re: Problems Calcuating Interest (Time value of money)
If you borrow \$1000 over 12 months and the payment is \$100 per month,
then the interest you paid HAS TO BE \$200, right?
Get it?

The dollar interest cost is evidently the total of the payments less the amount borrowed; ok?
• Sep 23rd 2012, 10:25 AM
jegues
Re: Problems Calcuating Interest (Time value of money)
Quote:

Originally Posted by Wilmer
If you borrow \$1000 over 12 months and the payment is \$100 per month,
then the interest you paid HAS TO BE \$200, right?
Get it?

The dollar interest cost is evidently the total of the payments less the amount borrowed; ok?

Okay, then why is it in this example,

For Q2), when we want to calculate how much we've paid in 20 peroids we did the future value of the payments for 20 peroids, not simply 20 * (payment amount)?

I want to be able to distinguish the two cases.
• Sep 23rd 2012, 10:39 AM
Wilmer
Re: Problems Calcuating Interest (Time value of money)
Quote:

Originally Posted by jegues
Okay, then why is it in this example,

For Q2), when we want to calculate how much we've paid in 20 peroids we did the future value of the payments for 20 peroids, not simply 20 * (payment amount)?

I want to be able to distinguish the two cases.

That's because we were not given the future value of the flows, which is 199,688.38;
the actual interest then is 199688.38 - 12000*5 - 6000*7
• Sep 23rd 2012, 11:51 AM
jegues
Re: Problems Calcuating Interest (Time value of money)
Quote:

Originally Posted by Wilmer
That's because we were not given the future value of the flows, which is 199,688.38;
the actual interest then is 199688.38 - 12000*5 - 6000*7

In my previous link I was refering to Q2) NOT Q1).

Can you try answering my previous question with reference to Q2) in the link?

Thanks again!
• Sep 23rd 2012, 01:15 PM
Wilmer
Re: Problems Calcuating Interest (Time value of money)
Quote:

Originally Posted by jegues
In my previous link I was refering to Q2) NOT Q1).
Can you try answering my previous question with reference to Q2) in the link?

Q2) A company borrowed \$100,000 to finance a new product. The loan was for 20 years at a nominal interest rate of 8 percent compounded semiannually. It was to be repaid in 40 equal payments. After one half of the payments were made, the company decided to pay the remaining balance in one final payment at the end of the 10th year. How much was owed?

The payment was calculated to be 5052.35
5052.35 * 40 = 202094.00 - 100000.00 = 102094.00 = interest if paid over the 20 years

Balance end of 10th year was calculated to be 68663.07
5052.35 * 20 = 101047.00 + 68663.07 = 169710.07 - 100000.00 = 69710.07 = interest if paid after 10 years.
• Sep 24th 2012, 05:15 AM
jegues
Re: Problems Calcuating Interest (Time value of money)
Quote:

Originally Posted by Wilmer
Q2) A company borrowed \$100,000 to finance a new product. The loan was for 20 years at a nominal interest rate of 8 percent compounded semiannually. It was to be repaid in 40 equal payments. After one half of the payments were made, the company decided to pay the remaining balance in one final payment at the end of the 10th year. How much was owed?

The payment was calculated to be 5052.35
5052.35 * 40 = 202094.00 - 100000.00 = 102094.00 = interest if paid over the 20 years

Balance end of 10th year was calculated to be 68663.07
5052.35 * 20 = 101047.00 + 68663.07 = 169710.07 - 100000.00 = 69710.07 = interest if paid after 10 years.

Okay but to solve that question we didn't do simply the payment amount times the number of peroids at the end of the 10th year, we did the future value of 100000.00 over 20 periods less future value of 20 payments of 5052.35.

Why is it that we need to calculate the future value and not simply do the payment amount times the number of peroids?
• Sep 24th 2012, 08:24 AM
Wilmer
Re: Problems Calcuating Interest (Time value of money)
Quote:

Originally Posted by jegues
Okay but to solve that question we didn't do simply the payment amount times the number of peroids at the end of the 10th year, we did the future value of 100000.00 over 20 periods less future value of 20 payments of 5052.35.

Why is it that we need to calculate the future value and not simply do the payment amount times the number of peroids?

Think about it.....the future value after 10 years IS ALSO A PAYMENT, since the loan is paid off at that time.