Question

$9,500 is invested in an account earning 9.1% interest (APR), compounded

quarterly. Write a function showing the value of the account after t years, where t
annual growth rate can be found from a constant in the function. Round all
coefficients in the function to four decimal places. Also, determine the percentage
growth per year (APY), to the nearest hundredth of a percent.

Answer 1

To have $10,000 in ten years with a 10% interest rate compounded annually, you would need to put approximately $3,854.07 into the bank account.

Step-by-step explanation:

To find the amount of money that needs to be invested to have $10,000 in ten years with a 10% interest rate compounded annually, we can use the formula for compound interest:

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

Where A is the final amount, P is the principal (initial amount), r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, we know the final amount A is $10,000, the annual interest rate r is 10% (or 0.10), and the number of times the interest is compounded per year n is 1. Let's solve for P:

P * 1.10^10 = $10,000

P = $10,000 / 2.5937

P = $3,854.07 (rounded to two decimal places)

Therefore, you would need to put approximately $3,854.07 into the bank account to have $10,000 in ten years with a 10% interest rate compounded annually.