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?

Guest Sep 8, 2020

#1**+1 **

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

ElectricPavlov Sep 8, 2020

#2**+1 **

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

Nacirema Sep 8, 2020

#4**+1 **

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

#5**+1 **

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.

Guest Sep 8, 2020