Question

Khalil is going to invest in an account paying an interest rate of 6.6% compounded daily. How much would Khalil need to invest, to the nearest dollar, for the value of the account to reach $1,470 in 9 years?

Answer 1

Khalil needs to calculate the initial investment (P) required to reach $1,470 in 9 years with an interest rate of 6.6% compounded daily by using the compound interest formula,
`A = P(1 + r/n)^(nt)`, and solving for P.

Step-by-step explanation:

To determine how much Khalil needs to invest today to have $1,470 in 9 years in an account with a 6.6% interest rate compounded daily, we need to use the formula for compound interest. The formula is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.

Since the interest is compounded daily, n would be 365, and r would be 0.066 (6.6% expressed as a decimal). Plugging in the desired amount ($1,470), the number of years (9), and the values for n and r into the formula, we first need to solve for P which leads to the equation
`A = P(1 + r/n)^(nt)`. By substituting our values, we get
`P = 1470 / (1 + 0.066/365)^(365*9)`. After calculating, we would round the result to the nearest dollar to find how much Khalil needs to invest today.

Answer 2

$1,000 to the nearest dollar

Step-by-step explanation:

We can use the formula for compound interest to calculate the amount that Khalil would need to invest:

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

where A is the final amount, P is the initial amount (the amount invested), r is the interest rate as a decimal (6.6% = 0.066), n is the number of times compounded in a year (daily = 365), t is the number of years, and ^ is the exponent operator.

We want to find P, so we can rearrange the formula:

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

Plugging in the values:

P = $1,470 / (1 + 0.066/365)^(365 * 9)

Calculating this expression to the nearest dollar, we get P = $1,000.

So, Khalil would need to invest $1,000, to the nearest dollar, in order for the value of the account to reach $1,470 in 9 years