Quick Math assistance.

[Sociopathic]

An annuity pays $1200 a year for 15 years. The money is invested at 5.2% compounded annually. The first payment is made 1 year after the purchase of the annuity. Determine the interest earned by the annuity over the 15 years.

Right. So the way I interpret this question is:

V = the future value of the investment
P = the principal investment amount
r = the annual interest rate
n = the number of times that interest is compounded per year
t = the number of years the money is invested for

So we have our V value as the value we're calculating.
P is the initial amount (1200)
R is the annual interest rate, represented as a DECIMAL (0.052) (Remember to get percentage to decimal divide by 100. 5.2/100 = 0.052)
N is the number of times it's compounded per year
And t is the number of years its invested for (15)

So putting that in, that gives me

1200(1+(0.052/1)^(1*15))

For easy calculating, the division by 1 in (0.052/1) and the multiplication by 1 in (1*15) is pointless, so I'll remove it.
1200*(1+0.052)^15
1200*(1.052)^15
1200*(2.139)

Which gives me $2566.95

Subtracting the initial amount (1200) is 1366.95.

Does this make sense. I'm stumbling because I am not sure 1200 is the initial amount put in, because it says "an annuity pays $1200 a year for 15 years."
What do?

[taliey]

This is a time value of money problem, right?

[Sociopathic]

This is a time value of money problem, right?

Uh... what? I'm not sure what you mean by this.

[Deleted]

Can you give me the equation used before you inputted the values. The symbols you used threw me off as they are the same for the ideal gas equation PV=nRT

Is that an exponential? x10^(15)

[Sociopathic]

Can you give me the equation used before you inputted the values. The symbols you used threw me off as they are the same for the ideal gas equation PV=nRT

Is that an exponential? x10^(15)

V = P(1+r/n)^nt

And no its not x10^15. Just ^15.

[taliey]

Uh... what? I'm not sure what you mean by this.

Yeah, I recognize what you're doing. You're trying to find the present value of future cash flows, AKA, present value of money.

That's what I meant.

[Sociopathic]

Yeah, I recognize what you're doing. You're trying to find the present value of future cash flows, AKA, present value of money.

That's what I meant.

Uh I am? I'm trying to find interest value over 15 years. The way the question was worded though is making me double take on my answer. "An annuity pays 1200 per year". So wtf doe sthat mean. I Gues the initial value isn't 1200 that I use up above? Not entirely sure what to make of it tbh. It would be easier if I had the book here with me, but I don't. Helping a friend online makes it very inconvenient.

[taliey]

Uh I am? I'm trying to find interest value over 15 years. The way the question was worded though is making me double take on my answer. "An annuity pays 1200 per year". So wtf doe sthat mean. I Gues the initial value isn't 1200 that I use up above? Not entirely sure what to make of it tbh. It would be easier if I had the book here with me, but I don't. Helping a friend online makes it very inconvenient.

I guess you're trying to find effective interest rates?

[dusselldorf]

I'm not familiar with annuities, but here's my assumption on first glance. If $1,200 is what the annuity pays and the interest rate is 5.2%, then the initial principle would be .052x=1,200, x= 23,076.92 where x is the initial principle. But that doesn't jive with the wording which says that the annuity pays 1,200 per year but is compounded annually. I have a feeling something is being left out, or I don't understand how annuities work, which is entirely possible.

[Dendrek]

An annuity pays $1200 a year for 15 years. The money is invested at 5.2% compounded annually. The first payment is made 1 year after the purchase of the annuity. Determine the interest earned by the annuity over the 15 years.

If I understand what you're saying correctly, each year the principle is increased by an additional $1200. If that's correct, then your calculation only included the initial amount. You didn't add in the effect of the additional payments.

To be clear,
1. If it's only one single initial investment, then 1200*(1.052)^15 - 1200 is correct.
2. If it's 1200 each year added to what's currently there, then it should be:

[1200*(1.052)^15 + 1200*(1.052)^14 + ... + 1200*(1.052)^2 + 1200*1.052] - [1200*15]

--------------- Edit ----------------

It appears this is a problem that involves two different investments (what I said above still applies if so), but please correct me if I'm wrong. The person in this problem purchased an annuity and is, himself, taking the money earned from that annuity and investing it into a savings account that gives a 5.2% compounded interest rate. Right?

--------------- Edit ----------------

In statement (2) above, the elipsis (...) means the pattern (1200*(1.052)^15 + 1200*(1.052)^14) repeats until it reaches the second part (1200*(1.052)^2 + 1200*1.052).

[Sociopathic]

If I understand what you're saying correctly, each year the principle is increased by an additional $1200. If that's correct, then your calculation only included the initial amount. You didn't add in the effect of the additional payments.

To be clear,
1. If it's only one single initial investment, then 1200*(1.052)^15 - 1200 is correct.
2. If it's 1200 each year added to what's currently there, then it should be:

[1200*(1.052)^15 + 1200*(1.052)^14 + ... + 1200*(1.052)^2 + 1200*1.052] - [1200*15]

--------------- Edit ----------------

It appears this is a problem that involves two different investments (what I said above still applies if so), but please correct me if I'm wrong. The person in this problem purchased an annuity and is, himself, taking the money earned from that annuity and investing it into a savings account that gives a 5.2% compounded interest rate. Right?

--------------- Edit ----------------

In statement (2) above, the elipsis (...) means the pattern (1200*(1.052)^15 + 1200*(1.052)^14) repeats until it reaches the second part (1200*(1.052)^2 + 1200*1.052).

Honestly this is the impression I was under as well, but I am not sure what the question is asking or if its a mistake. That kind of question goes beyond the scope of what the course is supposed to be, so I am confused as to whether its a significant typo or somebody screwed up somewhere. In any case, thanks for the assistance!

[Angella]

Annuity doesn't pay out until end of year 1, so no interest there. Year two you get interest from year 1 and another payment. Year 3 you get interest on year 1 and 2 and another payment. And so on. Thus:

year payment Year end total
1 1200 1200
2 1200 2462.4
3 1200 3790.4448
4 1200 5187.54793
5 1200 6657.300422
6 1200 8203.480044
7 1200 9830.061006
8 1200 11541.22418
9 1200 13341.36784
10 1200 15235.11896
11 1200 17227.34515
12 1200 19323.1671
13 1200 21527.97179
14 1200 23847.42632
15 1200 26287.49249

To get each new year just add the previous year, interest on previous year and the new payment. Eventually you get to year 15 and you subtract the total value at the end of year 15 from the net payments (1,200*15 = 18,000) and get $8,287.49.

- - - Updated - - -

Hm. I might have just done the inverse.

Upon 2nd reading, might be a straight Pr^t = payment plug. P is unknown. Rate is 1.054. T is 15 for 15 payment periods. payment is 1200*15 = 18,000. So:

P*1.054^15 = 18,000, or P = 8414.66. And then solving for interest earned you'd get 18,000 - 8,414.66 = 9,585.34.

[Dendrek]

Hm. I might have just done the inverse.

Upon 2nd reading, might be a straight Pr^t = payment plug. P is unknown. Rate is 1.054. T is 15 for 15 payment periods. payment is 1200*15 = 18,000. So:

P*1.054^15 = 18,000, or P = 8414.66. And then solving for interest earned you'd get 18,000 - 8,414.66 = 9,585.34.

After rereading, this actually makes more sense to me as well. I thought it strange he'd have to do iterative calculations.

[IIamaKing]

42

10 towels.

[Sociopathic]

Annuity doesn't pay out until end of year 1, so no interest there. Year two you get interest from year 1 and another payment. Year 3 you get interest on year 1 and 2 and another payment. And so on. Thus:

year payment Year end total
1 1200 1200
2 1200 2462.4
3 1200 3790.4448
4 1200 5187.54793
5 1200 6657.300422
6 1200 8203.480044
7 1200 9830.061006
8 1200 11541.22418
9 1200 13341.36784
10 1200 15235.11896
11 1200 17227.34515
12 1200 19323.1671
13 1200 21527.97179
14 1200 23847.42632
15 1200 26287.49249

To get each new year just add the previous year, interest on previous year and the new payment. Eventually you get to year 15 and you subtract the total value at the end of year 15 from the net payments (1,200*15 = 18,000) and get $8,287.49.

- - - Updated - - -

Hm. I might have just done the inverse.

Upon 2nd reading, might be a straight Pr^t = payment plug. P is unknown. Rate is 1.054. T is 15 for 15 payment periods. payment is 1200*15 = 18,000. So:

P*1.054^15 = 18,000, or P = 8414.66. And then solving for interest earned you'd get 18,000 - 8,414.66 = 9,585.34.

That might be the case. Thanks for your help!

This was just a very odd question. The second seems more on par with what the course would teach. Iterative calculations are . . not quite what it's about. But who knows.