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# annuity

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offered annunity that pays 3.9 % compound monthly. What equal monthly deposit should be made into this annunity in order to have \$79,000 in 18 years?

Sep 8, 2020

#1
+26628
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Assuming this is an annuity due (payments at beginning of month)

FV = P [(1+i)n -1]/i  *  (1+i)      i = .039/12     n = 18 yr * 12 months/yr = 216

P = 252.01

Sep 8, 2020
edited by ElectricPavlov  Sep 8, 2020
#3
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Yeah, sorry I didn't see this one before I posted. Go with this one. More likely to be correct.

Nacirema  Sep 8, 2020
#2
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Sorry, I don't get the problem that well. Here is my best shot at it:

There are 18 years and 12 months in each year. In order to calculate the amount warned per month, we will have to compute: \((75000/18)/12 \implies 9875/27\)

​​

After doing this, set x as the amount that has to be paid: \(.039x=9875/27\)

Then just compute:\(x=9377.9677113\)

Note: Electric Pavlov's answer is far more likely to be correct, so if ours are different, go with his/her's

Sep 8, 2020
#4
+110689
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Hi Naci,

This question is very poorly worded. The meaning must be guessed.

My guess:

An annuity pays 3.9 % (yearly and nominal (the effective rate is a little higher), compound monthly.

What equal monthly deposit should be made into this annuity in order (at the beginning of each month?) to have \$79,000 at the end of 18 years?

Anyway:

Your answer is far too simplistic. The money is going into an account each month and staying there for for 18 years.

18*12=216months      3.9/12=0.325% = 0.00325 interest per month

Assuming that the first installment is paid AT THE BEGINNING of the first month AND P dollars are deposited each month, then

the first deposit will grow to    P(1.00325)^216

the second deposit will grow to    P(1.00325)^215

...

the last deposit will grow to  P(1.00325)^1

You know that this will add to \$79000 so you can solve it as a GP (assuming you know about GPs geometric progressions)

There are also formulas, that I have forgotten,  EP has used a financial mathematics formula.

Melody  Sep 8, 2020
edited by Melody  Sep 8, 2020
#5
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Hi Melody: EP's calculation is correct if monthly payments are made at the beginning of each month.

FV=79000; R=0.039/12; N=18*12;PMT = FV*(((1 + R)^N - 1)^-1* R);print" PMT =\$",PMT

PMT =\$ 252.83 - Monthly payments made at the end of each month
PMT =\$ 252.01 - Monthly payments made at the beginning of each month.

Sep 8, 2020
#6
+110689
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I never suggested that EP was wrong.

If this was a school question here, the student would be expected to use a GP.

If it was a consumer finance question at a college then they would use the formula.

Melody  Sep 8, 2020
edited by Melody  Sep 8, 2020