Question

What EAR is being earned on a deposit of $5,000 made ten years ago today if the deposit is worth $9,948.94 today? The deposit pays interest semi-annually. A. 3.56 percent B. 6.76 percent C. 7.00 percent D. 7.12 percent

Answer 1

SOLUTION-

Initial deposit amount = $ 5,000

Value of the deposit after 10 years i.e., today = $ 9,948.94

Time period = 10 years or 20 semi annual years

Let r be the rate of interest per annum

We know that,

Future value = Present value ( 1 + r ) ^t

9948.94 = 5000 ( 1 + r /2 ) ²⁰

9948 / 5000 = (1+r/2 ) ²⁰⁼

1.9896 = (1+r/2 ) ²⁰

(1.9896)^1/20 = 1 + r/2

1.035 = 1 + r/2

1.035 - 1 = r/2

0.035 = r/2

0.035 * 2 = r

0.07 = r

r = 0.07 or 7 %

Hence EAR = 7 %

Therefore option (c) is correct.