Question

How much will he have to deposit as principal to have enough money in 1 year to buy the bike? Round your answer to the nearest cent.

In 1 year, Paco wants to buy a bicycle that costs $600.00. If he opens a savings account that earns 13% interest compounded continuously, how much will he have to deposit as principal to have enough money in 1 year to buy the bike?
Round your answer to the nearest cent.

Answer 1

$526.86

Explanation:

The formula for compound interest is `A=P(1+r/n)^(nt)` where `A` is the final amount, `P` is the principal amount, `r` is the interest rate as a decimal, `n` is the number of times compounded per year, and `t` is the time in years.

However, for continuous compounding.

Paco wants to buy a bike that costs $600.00, so `A=600`. His account's interest rate is 13%, so `r=0.13`. He wants to buy the bike in one year, so `t=1`.

Plugging these values into our formula, we get `600=Pe^(0.13cdot1)`. Rearranging to solve for `P`, we get `P=600/e^(0.13)` which we can plug into our calculator to find that `Papprox526.8573`, so Paco must invest $526.86.