Question

What is the maturity value of a 9-year term deposit of $4746.37 at 6.2% compounded semi-annually? how much interest did the deposit eam?

the maturity value of the term deposit is $ (round the final answer to the nearest cent as needed round all intermediate values to six decimal places as needed.)
the amount of interest earned is s (round the final answer to the nearest cent as needed. round all intermediate values to six decimal places as needed)

Answer 1

The maturity value of the term deposit is approximately $8772.46. The amount of interest earned is approximately $4026.09.

Step-by-step explanation:

To calculate the maturity value of a term deposit, we can use the formula:

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

Where:

• M is the maturity value
• P is the principal amount
• r is the interest rate per period
• n is the number of compounding periods per year
• t is the number of years

For the given term deposit:

• P = $4746.37
• r = 6.2% = 0.062
• n = 2 (compounded semi-annually)
• t = 9 years

Plugging in these values:

1. M = $4746.37 * (1 + 0.062/2)^(2 * 9)
2. M = $4746.37 * (1.031)^18
3. M ≈ $4746.37 * 1.8479659
4. M ≈ $8772.46

The maturity value of the term deposit is approximately $8772.46.

To calculate the amount of interest earned, we can subtract the principal amount from the maturity value:

1. Interest = M - P
2. Interest = $8772.46 - $4746.37
3. Interest ≈ $4026.09

The amount of interest earned is approximately $4026.09.