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

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

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.