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.

Explanation:

We apply the compound interest formula:

$FV\text{ = P(1 +}\frac{r}{n})^{nt}$

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{ + }\frac{0.1}{4})^{4\times3}$$\begin{gathered} 700=P(1+0.025)^{12} \\ 700=P(1.025)^{12} \\ 700\text{ = P(1.3449)} \end{gathered}$$\begin{gathered} \frac{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.