Question

bob deposits $5,000 at the end of each year in an ordinary annuity paying 12% interest compounded annually. find the amount he will have on deposit after 8 years. Round to the nearest dollar
a)$50,445
b)$61,498
c)56,498
d)73,878

Answer 1

For the first year, Bob gets 12% on his first deposit: 1.12(5000). The second year, Bob adds 5000 and gets 12% on top of what he had at the end of the first year plus his extra 5000 deposit: 1.12(1.12(5000) + 5000), if you expand this you get 1.12*1.12*5000 + 1.12*5000.

You can see a pattern here, so let's factor out the 5000 and see what the full 8 years would be:
5000(1.12^8 + 1.12^7 + ... + 1.12^2 + 1.12). Everything in the parentheses comes to approx. 14.775656, multiplied by 5000 gives you 73,878.28.

So D) $73,878 is your answer.

Answer 2

Hi there
The formula of the future value of annuity ordinary is
Fv=pmt [(1+r)^(n)-1)÷r]
Fv future value?
PMT payment per year 5000
R interest rate 0.12
N time 8 years

Fv=5,000×(((1+0.12)^(8)−1)÷(0.12))
Fv=61,498.46

So it's b

Good luck