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Nathaniel is going to invest in an account paying an interest rate of 3.1% compounded quarterly. How much would Nathaniel need to invest, to the nearest ten dollars, for the value of the account to reach $5,700 in 17 years?

Question

Nathaniel is going to invest in an account paying an interest rate of 3.1% compounded quarterly. How much would Nathaniel need to invest, to the nearest ten dollars, for the value of the account to reach $5,700 in 17 years?

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Solution

To solve this problem, we need to use the formula for compound interest, which is:

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

Where: A = the amount of money accumulated after n years, including interest. P = the principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = the time the money is invested for in years

We know that A = $5,700, r = 3.1% or 0.031 (in decimal), n = 4 (since the interest is compounded quarterly), and t = 17 years. We need to find P.

So, we rearrange the formula to solve for P:

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

Substituting the given values:

P = 5700 / (1 + 0.031/4)^(4*17)

Now, calculate the expression in the parentheses:

P = 5700 / (1 + 0.00775)^(68)

P = 5700 / (1.00775)^(68)

P = 5700 / 1.734

P = $3285.11

So, Nathaniel would need to invest approximately 3285tothenearesttendollars,forthevalueoftheaccounttoreach3285 to the nearest ten dollars, for the value of the account to reach 5,700 in 17 years.

This problem has been solved

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