Question

In 2 shane wants to buy a new bicycle that costs 700.00 if he opens a savings account that earns 6% interest compounded monthly how much will he have to despoit as principal to have enough money in 2 years to buy the bike

Answer 1

Compounded interest

We know that compounded interest is an accumulated interest during the next compounding period.

We know that it has a mathematical representation:

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

where,

A = the future value of the investment, including interest

P = the initial deposit amount

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per year

t = the time the money is invested

Shane wants to have $700.00 in two years, then

A = $700.00

t = 2 years

The account earns 6% interest compounded monthly, then

r = 6%/100 = 0.06

n = 12 (because it is compounded monthly and a year has 12 months)

We want to know how much will he have to despoit as principal to have enough money, it's to say, we want to find P.

Replacing the previous values in the equation:

`\begin{gathered} A=(1+(r)/(n))^(nt)P \\ 700=(1+(0.06)/(12))^(12\cdot2)P \\ 700=((12.06)/(12))^(24)P \\ 700=((12.06)/(12))^(24)P \\ 700=1.005^(24)P \\ 700\cdot1.005^(-24)=P \\ 621.03=P \end{gathered}`

Answer: he has to despoit $621.03