Question

In 3 Years Mateo wants to buy a bicycle that costs 700.00 if he opens a savings account that earns 10% interest compounded quarterly how much will have to deposite as principal to have enough money to buy the bike

Answer 1

He will need to deposit 520.48 as principal to have enough money to buy the bike.

Step-by-step explanation:

We apply the compound interest formula:

`FV\text{ = P(1 +}(r)/(n))^(nt)`

where FV = future value = money for bike = 700

r = rate = 10% = 0.1

n = number of time compounded

n = quaterly = 4

t = time = 3 years

P = principal = amount deposited = ?

`700\text{ = P}(1\text{ + }(0.1)/(4))^(4*3)`
`\begin{gathered} 700=P(1+0.025)^(12) \\ 700=P(1.025)^(12) \\ 700\text{ = P(1.3449)} \end{gathered}`
`\begin{gathered} (700)/(1.3449)=\text{ P} \\ P\text{ = 520.48} \end{gathered}`

He will need to deposit 520.48 as principal to have enough money to buy the bike.