Question

tyee is going invest in an account paying an interest rate of 4.7% compounded monthly. how much would tyee need to invest, to the nearest dollar, for the value of the account to reach 98,000 in 8 years

Answer 1

Tyee needs to invest a certain amount of money in an account with a 4.7% interest rate compounded monthly to reach $98,000 in 8 years. To find this initial investment, we use the compound interest formula and solve for the principal (P), then round the result to the nearest dollar.

Step-by-step explanation:

To determine how much Tyee needs to invest to have an account value reach $98,000 in 8 years with an interest rate of 4.7% compounded monthly, we can use the formula for compound interest:

`\[A = P \left(1 + (r)/(n)\right)^(nt)\]`

Where:

• A is the future value of the investment/loan, including interest.
• P is the principal investment amount (initial deposit or loan amount).
• 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 or borrowed for, in years.

In this case, we're solving for P and we have:

• A = $98,000
• r = 4.7% = 0.047 (as a decimal)
• n = 12 (since interest is compounded monthly)
• t = 8 years

Substituting these values into the formula gives us:

`\[98,000 = P \left(1 + (0.047)/(12)\right)^(12 \cdot 8)\]`

Calculating the right side of the equation:

`\[P = (98,000)/(\left(1 + (0.047)/(12)\right)^(96))\]`

After solving this on a calculator, you would round the final value to the nearest dollar to find the amount Tyee needs to invest initially.

The complete question is: tyee is going invest in an account paying an interest rate of 4.7% compounded monthly. how much would tyee need to invest, to the nearest dollar, for the value of the account to reach 98,000 in 8 years is:

Answer 2

To determine how much Tyee needs to invest to reach a value of $98,000 in 8 years with an interest rate of 4.7% compounded monthly, you can use the formula for compound interest. Plugging in the values, Tyee would need to invest $63,984 to the nearest dollar.

Step-by-step explanation:

To calculate how much Tyee would need to invest in order to reach a value of $98,000 in 8 years with an interest rate of 4.7% compounded monthly, we can use the formula for compound interest:

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

Where:

• A is the future value of the investment
• P is the principal amount (the initial investment)
• 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

In this case, we have:

A = $98,000

P is what we want to determine

r = 4.7% = 0.047

n = 12 (monthly compounding)

t = 8 years

Plugging in these values, we can solve for P:

$98,000 = P(1 + 0.047/12)^(12 * 8)

To the nearest dollar, Tyee would need to invest $63,984.