Question

Please show me how to do number 2.

$12,000 is deposited in a bank account that pays 9% nominal interest per year. Assume interest compounds monthly.

1. How much is in the account after 8 years?

(a) $24,600

(b) $25,200

(c) $26,300

(d) $27,700

2. What nominal annual interest would be required for the account to reach $30,000 in 8 years?

(a) 10.12%

(b) 10.88%

(c) 11.51%

(d) 12.26%

What nominal annual interest would be required for the account to reach $30,000 in 8 years?

Answer 1

1) We have an information that an amount worth $12,000 is deposited in a bank account at 9% nominal interest per year. Because the interest rate is compounds monthly, the effective rate is (1 + 9%/12)^12 - 1 = 9.3807%. After 8 years, the amount will worth F = 12000*(1 + 9.3807%)^8 = $24857. Option A is closest

2. Find the effective annual interest that would be required for the account to reach $30,000 in 8 years?

30000 = 12000*(1 + r%)^8

1 + r% = 1.121353

r% = 12.1353%. Now find the nominal interest rate as

12.1353% = (1 + i%/12)^12 - 1

(1.121353)^(1/12) = (1 + i%/12)

0.00959 = i%/12

This gives the nominal interest rate = 11.508% Option C is correct.