Question

Suppose you deposit $1,600 in an account with an annual interest rate of 6% compounded quarterly.

nt
Use the formula A = P(1 + )" and round each answer to 2 decimal places, if necessary.
3. Find an equation that gives the amount of money in the account after t years.
A (t) =
>. Find the amount of money in the account after 7 years.
After 7 years, there will be $
in the account.
How many years will it take for the account to contain $3,200?
It will take
years for there to be $3,200 in the account.
1. If the same account and interest were compounded continuously, how much money would the
account contain after 7 years?
With continuous compounding interest, there would be $
in the account after 7 years.

Answer 1

The amount of money in the account after 7 years with 6% interest compounded quarterly is $2,854.76. It will take approximately 11.9 years for the account to contain $3,200. With continuous compounding interest, the total after 7 years would be $2,673.85.

Step-by-step explanation:

To find the amount of money in an account with compound interest, we can use the formula A = P(1 + r/n)nt where:

• P is the principal amount (initial deposit),
• r is the annual interest rate (in decimal form),
• n is the number of times the interest is compounded per year,
• t is the number of years,
• A is the amount of money accumulated after n years, including interest.

For a $1,600 deposit at a 6% annual interest rate compounded quarterly (4 times a year), the equation is:

A(t) = $1,600(1 + 0.06/4)4t

Amount After 7 Years

Using the formula:

A(7) = $1,600(1 + 0.06/4)4*7 = $1,600(1 + 0.015)28 = $2,854.76

After 7 years, there will be $2,854.76 in the account.

Time to Double the Investment

To find out how many years it will take for the account to contain $3,200, we can set A(t) equal to $3,200 and solve for t:

$3,200 = $1,600(1 + 0.06/4)4t

t approximately equals 11.9 years.

Continuous Compounding Interest

If the account were compounded continuously, the formula A = Pert would be used where e is the base of the natural logarithms. After 7 years, the amount would be:

A = $1,600e0.06*7 = $1,600e0.42 = $2,673.85

With continuous compounding interest, there would be $2,673.85 in the account after 7 years.