Question

you invest 5000 in a bank savings account that pays 5% annual rate of interest. the interest is paid monthly. given this info how much will you have in 10 urs if in addition to 5000 you contribute an additional 2500 each year, at the end of the year

Answer 1

At the beginning of year 0 you have $5,000 in your account

at the end of the year, you'll have

`A=5000\cdot(1.05)=5250`

Then, at the beginning of year = 1 you will have $5,250 + $2,500 = $7,750

at the end of that year, you'll have

`A_1=7750\cdot1.05=8137.5`

Then, at the beginning of year = 2, you'll have $8137.50 + $2500 = $10,637.50

so, at the end of that year, you have:

`A_2=10637.5\cdot\: 1.05=11169.375`

Again, at the beginning of year 3, you'll have $11,169.375 + $2,500 = $13,669.375

so, at the end of that year, you have:

`A_3=13669.375\cdot\: 1.05=14352.84375`

If we continue doing so, until year 10, we will obtain the following

`\begin{gathered} A_4=17695.48594 \\ A_5=21205.26023 \\ A_6=24890.52325 \\ A_7=28760.04941 \\ A_8=32823.05188 \\ A_9=37089.20447 \\ A_(10)=41568.6647 \end{gathered}`

So, at the end of year 10, you'll have $41,568.66