Question

Determine the final account balance of an investment if $300 is invested at an interest rate of 6.75% p.a. compounded semiannually for 20 years. Pls show full working out ty

Answer 1

The final account balance of the investment would be approximately $939.38.

Step-by-step explanation:

To determine the final account balance of an investment, we can use the formula:

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

where:

• A is the final account balance
• P is the principal amount invested
• r is the interest rate in decimal form (6.75% = 0.0675)
• n is the number of times interest is compounded per year (semiannually = 2)
• t is the number of years the money is invested for (20 years)

Plugging in the values:

A = $300(1 + 0.0675/2)^(2*20)

Simplifying the exponent:

A = $300(1.03375)^(40)

Calculating the final account balance:

A ≈ $939.38

Answer 2

Account balance after 20 years will be
`\approx1131.73`

Step-by-step explanation:

`Given:\:P=300,\:r=0.0675,\:n=2,\:t=20\\\\A=P\left(1+(r)/(n)\right)^(nt)\\\\A=300\left(1+(0.0675)/(2)\right)^(2\cdot 20)\\\\A\approx1131.73`