Question

To redeem a $11 000.00 promissory note due in 12 years, george has set up a sinking fund earning 8% compounded semi-annually. equal deposits are made at the beginning of every six months. what is the size of the semi-annual deposits? question 13 options:

a. $568.22
b. $132.87
c. $246.03
d. 270.62
e. $2201.75
f. 300.11

Answer 1

To find the size of the semi-annual deposits, use the formula for the future value of an annuity. Plug in the given values and solve for P. The size of the semi-annual deposits is approximately $568.22.

Step-by-step explanation:

To find the size of the semi-annual deposits, we can use the formula for the future value of an annuity:

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

A is the future value, P is the deposit amount, r is the interest rate, n is the number of compounding periods per year, and t is the number of years. Given that the future value (A) is $11,000, the interest rate (r) is 8%, and the compounding is semi-annual (n = 2), we can plug in these values and solve for P:

$11,000 = P * ((1 + 0.08/2)^(2*12) - 1) / (0.08/2)

Simplifying this equation will give us the size of the semi-annual deposits, which is approximately $568.22.