# Using a TMV calculator to find out how to pay 2000/year over 20 years

#### FrizzleBear

##### New member
Question:
The Bondy family wishes to set up a scholarship fund. They would like to see 2000/year awarded over a 20 year period. It is expected that an investment could likely earn an average of 7.5% interest. How much must be invested now so that these awards can be granted? Show the TVM solver values.

---
N = 20I% = 7.5PV = 10972.46PMT = -2000FV = 40,000P/Y = 1C/Y = 1
If it were compounded annually, would I be correct?

#### Denis

##### Senior Member
Question:
The Bondy family wishes to set up a scholarship fund. They would like to see 2000/year awarded over a 20 year period. It is expected that an investment could likely earn an average of 7.5% interest. How much must be invested now so that these awards can be granted? Show the TVM solver values.

---
N = 20I% = 7.5PV = 10972.46PMT = -2000FV = 40,000P/Y = 1C/Y = 1
If it were compounded annually, would I be correct?

IF you're asking if $10972.46 is the correct PV of a$2000.00 annual
annuity over 20 years @ 7.5% annually, then NO !!

Why are you entering $40000 as FV? Should be ZERO. Consult your PVM manual. Keep playing around...when you get ~20389 as PV, then you will have "hit" the correct entries... Last edited: #### FrizzleBear ##### New member IF you're asking if$10972.46 is the correct PV of a $2000.00 annual annuity over 20 years @ 7.5% annually, then NO !! Why are you entering$40000 as FV? Should be ZERO.

Keep playing around...when you get ~20389 as PV, then you
will have "hit" the correct entries...

40,000 is FV because that would be the final value that I'm trying to reach through the 20 years of compound interest
My answer is probably wrong, but it's more of an issue with me not understanding the contents of the question

N = 20
I% = 7.5
PV =
20389
PMT =
N/A
FV = -86609.44
P/Y = 1
C/Y = 1

I'm not sure how this fits in with my question. Shouldn't my Final Value be 40,000 as that's what I'm trying to reach with my investments? I could invest much less to reach the 40k mark, as opposed to a PV of 20k, right?

#### Denis

##### Senior Member
Sorry; got no idea what you're doing/entering...

In case it helps you, here's the "picture":
Code:
YEAR  PAYMENT  INTEREST  BALANCE
0                      20389.00
1  -2000.00   1529.18  19918.18  : 20389.00 * .075 = 1529.18
2  -2000.00   1493.86  19412.04  : 19918.18 * .075 = 1493.86
....
18  -2000.00    390.08   3591.12
19  -2000.00    269.34   1860.46  :  3591.12 * .075 = 269.34
20  -2000.00    139.54       .00  :  1860.46 * .075 = 139.54
In other words, $20389.00 is deposited in a 7.5% annual interest account, and this permits 20 annual withdrawals (or payments) of$2000.00

The Future Value is clearly ZERO (end of 20th year).
It'll all come to you later...as you learn from your teacher...

#### Denis

##### Senior Member
N = 20
I% = 7.5
PV =
20389
PMT =
N/A
FV = -86609.44
P/Y = 1
C/Y = 1

I'm not sure how this fits in with my question. Shouldn't my Final Value be 40,000 as that's what I'm trying to reach with my investments? I could invest much less to reach the 40k mark, as opposed to a PV of 20k, right?
Try this way:
enter the number of years: 20
enter the annual payment: 2000
enter the future value: ZERO
enter the rate: 7.5
Output should be 20389 as PV

#### Dr.Peterson

##### Elite Member
40,000 is FV because that would be the final value that I'm trying to reach through the 20 years of compound interest

Shouldn't my Final Value be 40,000 as that's what I'm trying to reach with my investments? I could invest much less to reach the 40k mark, as opposed to a PV of 20k, right?

I think you're confusing the fact that the total of the amounts you want to take out from the fund over 20 years is $40,000, with what you want to be left in the fund after the 20 years. The plan is to use up all the money over those 20 years by taking it out$2000 at a time (payments). You don't want any money left over at the end (future value).

#### FrizzleBear

##### New member
Ok. I understand it now. Thanks everyone.

#### Atenas

##### New member
Code:
YEAR  PAYMENT  INTEREST  BALANCE
0                      20389.00
1  -2000.00   1529.18  19918.18  : 20389.00 * .075 = 1529.18
2  -2000.00   1493.86  19412.04  : 19918.18 * .075 = 1493.86
....
18  -2000.00    390.08   3591.12
19  -2000.00    269.34   1860.46  :  3591.12 * .075 = 269.34
20  -2000.00    139.54       .00  :  1860.46 * .075 = 139.54
In other words, $20389.00 is deposited in a 7.5% annual interest account, and this permits 20 annual withdrawals (or payments) of$2000.00

The Future Value is clearly ZERO (end of 20th year).
That's correct.

PV = PMT(1-(1+i))^-n / i =
PV =2000(1-(1+0.075)^-20 / 0.075 = $20,388.98 I = n * PMT I = 20 * 2000 =$40,000.00 - $20,388.98 =$19,611.02

N = 20
I% = 7.5
PV = 20,388.98
PMT= 2000
FV = 0
P/Y= 1
C/Y= 1