Question

1. An investor deposits $400 into a bank account that earns an annual interest rate of 8%. Based on this information, how much interest will he earn during the second year alone? (choose a or b)

a. 32 b. 34.56

2. A monthly interest rate of 1% is a compounded annual rate of:

a. 12.5 b. 12.68

3. Suppose that a family wants to save money for a child's college tuition. The child will be attending college in 12 years. The cost of college education today is $120,000. If the interest rate is 6% and the inflation rate is 2%, then about how much does this family need to deposit in their savings account today?

a. 75633  b. 74420

4. Sharon deposits $150.00 in her savings account at the bank. At the end of one year she has $156.38. What was the interest rate that Sharon earned?

a. 4.3 b. 4.25

<please write down the explaination>

Answer 1

1. Amount deposited today = $ 400; 1st year interest on $ 400 = $ 400 * 8% = $ 32. Therefore, account balance for year 2 interest calculation = $ 400 + $ 32 = $ 432. Hence, 2nd year interest will be at 8% on $ 432 = $ 432*8% = $ 34.56.

So, the correct answer in Option b $ 34.56

2. 1% monthly interest rate when compounded then it will be equal to [(1+0.01)^12 - 1]. On solving we get value as 0.1268 or 12.68%

So, the correct answer for this is Option b 12.68

3. $ 120,000 is the present value of college fees and the child will attend college after 12 years, so we use Present value formula with inflation that is PV = FV/ {(1+r)/(1+i)}^n

here, FV = 120000, r = 6% or 0.06, inflation, i = 2% or 0.02 and n = 12 years

therefore, PV = 120000/ {(1+0.06)/1+0.02)}^12 = $ 75,633.27 or $ 75,633

So, the correct answer is Option a $ 75,633

4. Value of $ 1 deposited today at r% rate of return after n years of invest at simple interest becomes 1*(1+r)^n;

Here, we have n = 1 year, investment amount = $ 150 and Maturity Amount after 1 year = $ 156.38 and if rate of interest is r then; 156.38 = 150*(1+r)^1 or 156.38 = 150 + 150*r or 6.38 = 150*r or r = 6.38/150 = 0.42533 or we can say that rate of return is 4.2533% or 4.25%

So, the correct answer to this is Option b 4.25%