Question

Lynn Ally, owner of a local Subway shop, loaned $58,000 to Pete Hall to help him open a Subway franchise. Pete plans to repay Lynn at the end of 6 years with 8% interest compounded semiannually. How much will Lynn receive at the end of 6 years? (Use the Table provided.) Note: Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

The formula for calculating the future value of an investment with compound interest is: FV = PV × (1 + r/n)^(n*t)

Where FV is the future value, PV is the present value, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

Using this formula, we can calculate the future value of Pete's loan:

PV = $58,000

r = 8% = 0.08

n = 2 (compounded semiannually)

t = 6 years

FV = $58,000 × (1 + 0.08/2)^(2*6)

FV = $58,000 × 1.593848

FV = $92,410.64

Therefore, Lynn will receive $92,410.64 at the end of 6 years

Answer 2

The future value of the loan that Lynn will receive at the end of 6 years can be calculated using the formula for compound interest, substituting the relevant values into the formula and rounding the final result to the nearest cent.

Pete plans to repay Lynn $58,000 at the end of 6 years with 8% interest compounded semiannually. To calculate the future value of this loan, we use the formula for compound interest:

FV = P(1 + r/n)(nt)

Where:

P is the principal amount ($58,000)

n is the number of times the interest is compounded per year (2)

t is the time the money is invested for in years (6)

Substituting the values into the formula gives us:

FV = 58000(1 + 0.08/2)(2 * 6)

Calculating further, we find:

FV = 58000(1 + 0.04)12

FV = 58000(1.04)12

After calculating the value inside the bracket to its 12th power and then multiplying by 58000, we will get the amount Lynn will receive at the end of 6 years. Round the final amount to the nearest cent.