Question

How do I solve this 2 part problum? 1) An annuity is a system where you deposit the same amount each month, and the amount you have at the end of the year is given by Sn where if the APR is 12%, r=1.01, and n=12. You deposit $100 per month. What is the total in the annuity at the end of the year?2)the bank does continuous interest using Sn=(a(1-e^qn)/(i-e^q)) where q=1.01 find the amount. Do they match?

Answer 1

me dont beleev APR=12%.

Yu talk bout akkount yu hav with a bank, weer bank pae yu interest

In tudaes werld, yu mite get 1% or 2% on yer savings

Me also dont beleev em pae yu "kontinyuus"...no bank du that

Month kompound is kommon or 1 time per yeer

If yu put in 100$/month with 1% interest for 1 yeer, yu will hav 1,206.52$ (interest kompound bi month)

Answer 2

Part 1 using Sn = [ a ( 1 - r ^n ) ] / 1 - r is solved like this:

Sn = [ a ( 1 - r ^n ) ] / 1 - r

1. = { $100. [ 1 - (1.01^12)] } / 1 - 1.01
2. ~ { $100. [ 1 - (1.1268) ] } / 1 -1.01
3. ~ [ $100. ( 1 -1.1268 ) ] / -0.01
4. ~ [ $100. ( -0.1268 ) ] / -0.01
5. ~ ( - $12.68 ) / -0.01
6. ~ $1268.

And part 2 is solved like this:

Sn = [ a ( 1 - e^qn ) ] / (1 - e^q)

1. = { $100 [ 1 - ( 1.01^1.01*12 ) ] } / [ 1 - ( 1.01^1.01 ) ]
2. = { $100 [ 1 - ( 1.01^12.12 ) ] } / [ 1 - ( 1.01^1.01 ) ]
3. ~ { $100 [ 1 - ( 1.1282 ) ] } / [ 1 - ( 1.0101 ) ]
4. ~ [ $100 ( 1 -1.1282 ) ] / ( 1 -1.0101 )
5. ~ [ $100 ( -0.1282 ) ] / ( -0.0101 )
6. ~  ( - $12.82 ) / ( -0.0101 )
7. ~ $1269.31

My calculations say they do not match but are close to each other.