Question

**18**-a) What would be the future value of $18,000
invested now if the money remains deposited for eight years, the
annual interest rate is 18 percent, and interest on the investment
is compounded semi-annually?

b) How would your answer for (a) change if quarterly compounding were used?

Answer #1

**18.a. The future value is computed as shown
below:**

**Future value = Present value (1 +
r) ^{n}**

**r is computed as follows:**

= 18% / 2 (Since the interest is compounded semi annually, hence divided by 2)

**= 9% or 0.09**

**n is computed as follows:**

= 8 x 2 (Since the interest is compounded semi annually, hence multiplied by 2)

**= 16**

**So, the amount will be computed as follows:**

= $ 18,000 x 1.09^{16}

**= $ 71,465.51 Approximately**

**18.b. The future value is computed as shown
below:**

**Future value = Present value (1 +
r) ^{n}**

**r is computed as follows:**

= 18% / 4 (Since the interest is compounded quarterly, hence divided by 4)

**= 4.5% or 0.045**

**n is computed as follows:**

= 8 x 4 (Since the interest is compounded quarterly, hence multiplied by 4)

**= 32**

**So, the amount will be computed as follows:**

= $ 18,000 x 1.045^{32}

**= $ 73,619.66 Approximately**

Feel free to ask in case of any query relating to this question

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