Question

In 3 Years ago 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 he have to despoit as principal to have enough money in 3 years to buy the bike

Answer 1

He have to deposit $520.49 as Principal to have enough money in 3 years to buy the bike.

`\text{ \$520.49}`

Step-by-step explanation:

The formula for calculating the Future value of Compound interest is;

`A=P(1+(r)/(n))^(nt)`

Where;

A = Future Value/Amount

P = Principal

r = Interest rate (decimal)

n = number of times the interest is compounded per unit time "t"

t = Time

Making the Principal P the subject of formula;

`P=(A)/((1+(r)/(n))^(nt))`

Given;

A = $700.00

r = 10% = 0.10

n = compounded quarterly (4 times a year) = 4

t = 3 years

substituting the given values;

`\begin{gathered} P=\frac{\text{ \$700.00}}{(1+(0.10)/(4))^(4(3))}=\frac{\text{ \$700.00}}{(1.025)^(12)} \\ P=\text{ \$520.49} \end{gathered}`

Therefore, he have to deposit $520.49 as Principal to have enough money in 3 years to buy the bike.

`\text{ \$520.49}`