Question

in 3 years leory wants to buy a bicycle that costs $1,000.00 . if he opens a savings account that earns 10% interest compounded monthly how much will he have to despoit as principal to have enough money in 3 years to buy the bike

Answer 1

In order to find the deposit Leory needs to make, let's use the following formula for compound interest:

`C=A\cdot(1+(i)/(n))^(nt)`

Where C is the final value, A is the initial value, i is the interest rate, t is the time and n is a constant related to the period of interest.

For this case, we have C = 1000, i = 10% = 0.1, n = 12 (the interest is compounded monthly), and t = 3, so we have that:

`\begin{gathered} 1000=A(1+(0.1)/(12))^(12\cdot3) \\ 1000=A(1+0.008333)^(36) \\ 1000=A(1.008333)^(36) \\ 1000=A\cdot1.34818 \\ A=(1000)/(1.34818)=741.74 \end{gathered}`

So the initial deposit is $741.74.