Question

Henry needs $9401 for a future project. He can invest $7000 now at an annual rate of 7%, compounded quarterly. Assuming that no withdrawals are made,

how long will it take for him to have enough money for his project?
Do not round any intermediate computations, and round your answer to the nearest hundredth.
years
X

Answer 1

Henry's investment of $7000 at an annual interest rate of 7%, compounded quarterly, will reach $9401 in approximately 4.74 years.

Step-by-step explanation:

Henry needs $9401 for a future project, and he wants to know how long it will take for his current investment of $7000 at an annual rate of 7%, compounded quarterly, to reach that amount. The formula for compound interest is:

`A = P (1 + r/n)^(^n^t^)`

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.
• t is the time the money is invested for in years.

To find t, we rearrange the formula to solve for t:

t = (log(A/P)) / (n*log(1 + r/n))

Plugging in the values:

• P = $7000
• A = $9401
• r = 0.07 (7% annual interest rate)
• n = 4 (compounded quarterly)

We get:

t = (log(9401/7000)) / (4*log(1 + 0.07/4))

After performing the calculations, we find that t is approximately 4.74 years. So, Henry will need to wait about 4.74 years for his investment to grow to $9401.