Question

Katherine is going to invest in an account paying an interest rate of 5.8% compounded monthly. How much would Katherine need to invest, to the nearest ten dollars, for the value of the account to reach $960 in 16 years?

Answer 1

Katherine would need to invest approximately $481.18 for the value of the account to reach $960 in 16 years.

Step-by-step explanation:

To find out how much Katherine would need to invest, we can use the compound interest formula:

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

Where:

• A is the amount in the account after time t
• P is the principal (initial investment)
• r is the interest rate (as a decimal)
• n is the number of times interest is compounded per year
• t is the number of years

In this case, Katherine wants the account to reach $960 in 16 years, and the interest rate is 5.8% compounded monthly. Plugging in these values and solving for P:

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

P = $960 / (1 + 0.058/12)^(12*16)

P ≈ $960 / (1 + 0.004833)^192

P ≈ $960 / 1.996685

P ≈ $481.18

Therefore, Katherine would need to invest approximately $481.18 for the value of the account to reach $960 in 16 years.