Question

*. Il you invest $50,000 to earn 8% interest, which of the following compounding approaches would return the highest amount after one year? a. Annually b. Quarterly c. Monthly d. Daily 5. Assume ABC Company deposits $20,000 with First National Bank in an account earning interest at 8% per annum, compounded quarterly. How much will ABC have in the account after 3 years? (Use the factor tables provided at the end. Round answers to the nearest whole dollar) a. $25,194 b. $25,306 c. $25,365 d. $26,898 6. Barkley Company will receive $16,000 in a future year. If the future receipt is discounted at an interest rate of 4% annually, its present value is $10,000. In how many years will the $16,000 be received? (Use the factor tables provided at the end. Choose the closest answer) a. 11 years b. 12 years c. 13 years d. 16 years 7. Lucy and Fred want to begin saving for their baby's college education. They estimate that they will need $200,000 in 6 years. If they are able to earn 10% per year, how much must be deposited at the end of each 6 months to fund the education? (Use the factor tables provided at the end. Round answers to the nearest whole dollar.) a. $12,565 b. $11,367 c. $15,174 d. $28,674

Answer 1

4. The compounding will generate the high amount in directly proportional manner, as the number of compounding increases the yield increases proportionately in increasing pattern. Therefore compounding daily will return highest amount after one year.

5. The formula for calculating the amount as per compounding is A = p(1+r/n)^nt ​​​​​​, where a is the amount including interest, p is the principal amount, r is the interest rate, n is the number of compoundings per annum, t is number of years. Substituting the values as p=20000, n=compounding quarterly = 4, t = 3years, r = 8%, therefore amount after 3 years = 20000(1+8%/4)^3*4 = 25,365.

6. For calculating time period we shall use the formula A = p{1+r/n)^nt, substituting the values 16000 = 10000(1+4%/1)t, therefore 1.6 = (1.04)^t, now t can be arrived at by multiplying 1.04 by itself till we get 1.6, i have used my calculator but you can use the tables given, and the answer is 12 years.

7. The amount to be invested every 6 months to get a fixed amount in the future is known as annuity and the question is about ordinary annuity as it is calculated for end of the period, the formula is F = p((1+r)ⁿ​​​​​​-1)/r, where f is the future value that is 200,00 p is the installment which is to be calculated, r = 10%/2 = 5% half yearly, and n = 2 half yearly. Substituting the values 200000 = p((1+5%)²-1)/5% therefore p = 12,565, the requirement is 12,565.