Question

1. You won $100 000 in a lottery and you want to set some of that sum aside for 10 years. After 10 years, you would like to receive $2400 at the end of every 3 months for 8 years. How much of your winnings must you set aside if interest is 5.5% compounded quarterly? 2. A sum of money is deposited at the end of every month for 10 years at 7.5% compounded monthly. After the last deposit, interest for the account is to be 6% compounded quarterly and the account is to be paid out by quarterly payments of $4800 over six years. What is the size of the monthly deposit? 3. Compute the nominal annual rate of interest compounded semi-annually on a loan of $48 000 repaid in installments of $4000 at the end of every 6 months in 10 years. 4. A loan of $14 400 is to be repaid in end-of-the-quarter payments of $600. How many payments are required to repay the loan at 10.5% compounded quarterly? 5. The amount of $574 is invested monthly at 6% compounded monthly for six years. The balance in the fund is then converted into an annuity paying $3600 at the end of every three months. If interest on the annuity is 5.9% compounded quarterly, for how many months is the term of the annuity? 6. A loan was repaid over seven years by end-of-month payments of $450. If interest was 12% compounded monthly, how much interest was paid? 7. Ms. Simms made deposits of $540 at the end of every three months into a savings account. For the first five years interest was 5% compounded quarterly. Since then the rate of interest has been 5.5% compounded quarterly. How much is the account balance after 13 years? 8. How much interest is included in the accumulated value of $3200 paid at the end of every six months for four years if the interest rate is 6.5% compounded semi-annually? 9. What is the size of deposits made at the end of each period that will accumulate to $67 200 after eight years at 6.5% compounded semi-annually? 10. Explain all types of annuities that you learned in this chapter

Answer 1

Data given in the first question to find out the amount to be invested for withdrawing a $2400 at every quarter at equal intervals for 8 years after the 10th year of investment made now

I = 5.5 % Compounded Quarterly

I = 5.5%/4 = 0.013875

n = 10 years * 4 = 40

and to calculate PV , n = 8 years * 4 = 32

So , P (1+0.013875) ^40 = R [1-(1.013875)^-32]

                                                ___________________

                                                                0.013875

                                                = 2400(0.3605/0.013875)

                                                = 2400 X 25.98

                                                = $ 62356.47

P = 62356.47 /1.7353 = $ 35934.12