Present Value, Future Value, Rate

**fw_mathis** · June 5th 2007, 09:26 AM

Hello. I am having a hard time determining which function I should be using to solve these problems. Can someone please put me on the right track????? Thanks to anyone that can help me.

Problem 1: Joe won a lottery jackpot that will pay him $12,000 each year for the next ten years. The market rate is currently 12%. How much does the lottery have to invest today to pay out this prize to Joe over the next ten years?

Problem 2: Mary just deposited $33,000 in an account paying 10% interest. She plans to leave the money in this account for seven years. How much will she have in her account at the end of the seventh year?

Problem 3: Mary and Joe would like to save up $10,000 by the end of three years from now. They currently have $2500 in a savings account. They would like to make equal year end deposits to this savings account to pay for furniture when they purchase it three years from now. This account pays 8% interest. How much should the year end payments be?

**janvdl** · June 5th 2007, 09:42 AM

Problem 2: Mary just deposited $33,000 in an account paying 10% interest. She plans to leave the money in this account for seven years. How much will she have in her account at the end of the seventh year?

$A = P(1 + \frac{i}{100})^n$

$A = (33 000)(1 + \frac{10}{100})^7$

$A = 64 308$

**Soroban** · June 5th 2007, 10:32 AM

Hello, fw_mathis!

Here are the first two . . .

I must assume you are familiar with all the necessary formulas:
. . compound interest, annuities, amortization, etc.

1) Joe won a lottery jackpot that will pay him $12,000 a year for the next 10 years.
The market rate is currently 12%. .How much does the lottery have to invest today
to pay out this prize to Joe over the next ten years?

The amortization formula is: . $A \:=\:P\frac{i(1+i)^n}{(1+i)^n-1} \quad\Rightarrow\quad P \;=\;A\frac{(1+i)^n - 1}{i(1+i)^n}$

. . where: . $\begin{array}{ccc}A & = & \text{periodic payment} \\ P & = & \text{principal invested} \\ i & = & \text{periodic interest rate} \\ n & = & \text{number of periods} \end{array}$

So we have: . $P \;=\;12,\!000\!\cdot\!\frac{(1.12)^{10} - 1}{0.12(1.12)^{10}} \;\approx\;\$67,802.68$

2) Mary just deposited $33,000 in an account paying 10% interest.
She plans to leave the money in this account for seven years.
How much will she have in her account at the end of the seventh year?

This is just compound interest: . $A \;=\;P(1 + i)^n$

We have: . $P = 33,\!000,\:i = 0.10,\:n = 7$

Therefore: . $A \;=\;33,\!000(1.10)^7 \;\approx\;\$64,307.66$

**janvdl** · June 5th 2007, 10:35 AM

I messed up on that first one, thanks Soroban

**neverlosehope** · June 16th 2007, 12:50 PM

if a person was indebted for $200 that was due after six months & $300 due after one year. if the lender approved of an 18% interst rate per year.Calculate the amount the borrower should pay now.
if the borrower decided to pay both of the amounts after one year from now. calculate the amount he should pat in that date

**neverlosehope** · June 16th 2007, 12:53 PM

Hi ,plz i need ur help .i have an exam after couple of hours.

if a person was indebeted for $200 that was due after six months & $300 due after one year. if the lender approved of an 18% interst rate per year.Calculate the amount the borrower should ppay now.
if the borrower decided to pay both of the amounts after one year from now. calculate the amount he should pat in that date

plz help me soroban...

**Jhevon** · June 16th 2007, 12:59 PM

Originally Posted by neverlosehope

Hi ,plz i need ur help .i have an exam after couple of hours.

if a person was indebeted for $200 that was due after six months & $300 due after one year. if the lender approved of an 18% interst rate per year.Calculate the amount the borrower should ppay now.
if the borrower decided to pay both of the amounts after one year from now. calculate the amount he should pat in that date

plz help me soroban...

your question seems to have information missing, or is at least, not phrased correctly. Please use the exact wording of the question

Also, please post new questions in a new thread, it's harder for your post to get noticed attaching it to someone else's thread

**neverlosehope** · June 16th 2007, 01:16 PM

sorry yeah there is somthing wrong one min
it's not that one

**neverlosehope** · June 16th 2007, 01:22 PM

If a person borrowed $2000 at 15%on the first of June 2000 to pay it in two equal times: the first on December 1st, 2000 & the other on June 1st,2001 & if the datum date was June 1st,2000. Calculate the value of each payment
if the datum date was changed to be 1/6/2001.calculate the value of each payment.

Using the rule

p= m/(1+rt)[
or M= p(1+rt

**Jhevon** · June 16th 2007, 01:44 PM

Originally Posted by neverlosehope

[FONT='Verdana','sans-serif']If a person borrowed $2000 at 15%on the first of June 2000 to pay it in two equal times: the first on December 1st, 2000 & the other on June 1st,2001 & if the datum date was June 1st,2000. Calculate the value of each payment.[/font][FONT='Verdana','sans-serif']

Using the rule
p= m/(1+rt)
or M= p(1+rt)[/font]

the interest is applied once every 6 months. he has 1 year to pay it off. so that's two 6 month periods, so the interest would be applied twice. thereofre, t = 2 over all. but we want each payment, so we take t = 1, for the first payment, and t = 1 for the second as well. the rate r, is the percentage written as a decimal, so r = 15% = 0.15. p is the principal, which is the original amount, so p = 1000 (since we have 2 equal installments. M is the amount owed after the said period. so just plug these into the formula.

Both payents would be the same, so let's just find the first:

$M_1 = p( 1 + rt)$

$\Rightarrow M_1 = 1000(1 + (0.15)(1))$

$\Rightarrow M_1 = 1150$

So the two payments are:

$M_1 = M_2 = 1150$

if the datum date was changed to be 1/6/2001.calculate the value of each payment.

the phrase "datum date" is unfamiliar to me, but i suppose it just means that the interest is applied after the year is up.

we would use r = 0.15, t = 1/2, p = 1000 for each payment, in the same formula. we would get each payment to be 1075

**neverlosehope** · June 16th 2007, 03:05 PM

i have the anser but i don't understand it
X=1111.24

& the second part of the question X=11o8.23

**Jhevon** · June 16th 2007, 03:16 PM

Originally Posted by neverlosehope

i have the anser but i don't understand it
X=1111.24

& the second part of the question X=11o8.23

i dont see how those can be the answer either

**neverlosehope** · June 16th 2007, 03:19 PM

[FONT='Times New Roman','serif']If a person borrowed $2000 at 15%on the first of June 2000 to pay it in two equal times: the first on December 1st, 2000 & the other on June 1st,2001 & if the datum date was June 1st,2000. Calculate the value of each payment[/FONT][FONT='Times New Roman','serif'][/FONT]

[FONT='Times New Roman','serif']X??[/FONT]
[FONT='Times New Roman','serif']p= m/(1+rt)[/FONT]
[FONT='Times New Roman','serif']2000= X/(1+0.15*6/12) + X/(1+0.15*12/12)[/FONT]
[FONT='Times New Roman','serif']2000= 2.225x /1.23625[/FONT]
[FONT='Times New Roman','serif']2.225X=2472.5[/FONT]
[FONT='Times New Roman','serif']So, X=2472.5/2.225 = 1111.24[/FONT]
[FONT='Times New Roman','serif'][/FONT]
[FONT='Times New Roman','serif']if the datum date was changed to be 1/6/2001.calculate the value of each payment.[/FONT]
[FONT='Times New Roman','serif']M= p(1+rt)[/FONT]
[FONT='Times New Roman','serif']M= 2000 (1+0.15*1)= 2300[/FONT]
[FONT='Times New Roman','serif']So, 2300 = X (1 + 0.15 * 6/12) + X[/FONT]
[FONT='Times New Roman','serif']2300=2.075 X[/FONT]
[FONT='Times New Roman','serif']X= 1108.43 [/FONT]

**neverlosehope** · June 16th 2007, 03:22 PM

If a person borrowed $2000 at 15%on the first of June 2000 to pay it in two equal times: the first on December 1st, 2000 & the other on June 1st,2001 & if the datum date was June 1st,2000. Calculate the value of each payment.

X??

p= m/(1+rt)
2000= X/(1+0.15*6/12) + X/(1+0.15*12/12)
2000= 2.225x /1.23625
2.225X=2472.5
So, X=2472.5/2.225 = 1111.24
if the datum date was changed to be 1/6/2001.calculate the value of each payment
M= p(1+rt)
M= 2000 (1+0.15*1)= 2300
So, 2300 = X (1 + 0.15 * 6/12) + X
2300=2.075 X

X= 1108.43

**neverlosehope** · June 16th 2007, 03:34 PM

I can't understand it plz explain thsi answer

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