Annuity and Future Value Problems in Compound Interest - Examples and Solutions

Q1 How much will you have in 8 years by investing $350 at the end of every month into an investment that earns 4.8% compounded monthly?

Q2 An ordinary annuity consists of 50 semi-annual deposits of $700. What is the future value of the annuity if it earns interest at the rate of 6% compounded semi-annually for the first 15 years and 8% compounded semi-annually for the last 10 years?

Q3 An ordinary annuity with an opening balance of $6,000 receives quarterly deposits of $500 for during the first 6 years. Find the future value of this annuity if it earns interest at the rate of 5% compounded quarterly and the fund matures in 10 years time.

Q4 How much will you pay for an ordinary annuity that will pay you $5,000 every 3 months for 15 years? Use an interest rate of 6% compounded quarterly for your calculation.

Q5 How much money will you need to have in an account today if you wish to withdraw $1,000 at the end of each month for the first 10 years and then $1,500 at the end of each month for an additional ten years? Assume that you can earn interest at 6% compounded monthly throughout.

PV Annuity (Solve for PV, PMT, n, j1 and jm):

A two-year auto lease requires payments of $550 at the beginning of each month. Calculate the present value of these lease payments using an interest rate of 6.5% compounded monthly.

Q6 What would be your quarterly payments for a $3,500 two-year loan if the interest rate charged is 4.75% compounded quarterly?

Q7 You purchase an annuity for $214,600. The interest rate earned by the annuity is 6.5% compounded monthly. How many end of month payments of $1,600 will you receive?

A $13,500, five-year loan requires monthly payments of $300.00.  

(a) What is the nominal rate of interest compounded monthly and 

(b) What is the effective rate of interest on this loan?

Q8 How much money will you need to have in an account today if you wish to withdrawal $1,000 at the end of each quarter for the first 5 years and then $1,500 at the end of each quarter for another ten years. Assume that you can earn interest at 7% compounded quarterly throughout.

FV Annuity (Solve for FV, PMT, n, j1and jm):

Q1

Q9 How much will you have in 8 years by investing $350 at the end of every month into an investment that earns 4.8% compounded semi-annually?

Q10 How much do you need to deposit semi-annually for 3 years, at 6% compounded quarterly, to accumulate $3,000.00? 

Q11 How long will it take for end-of-quarter deposits of $400 to accumulate to $25,000 in an investment account that earns 4.4% compounded quarterly?

Q12 How long will it take for semi-annual deposits of $1,675 to accumulate to $20,000 in an investment account that earns 3.25% compounded monthly? 

Q13 If your investments of $1,000 at the end of each year have grown to $10,500 over the past 8 years what is effective rate of interest are you earning?

FV Annuity Problems – challenge

Q14 An ordinary annuity consists of 50 semi-annual deposits of $700. What is the future value of the fund if it earns interest at the rate of 8% compounded semi-annually for the first 10½ years and 6% compounded quarterly for the remainder of the term? 

Q15 An ordinary annuity with an opening balance of $6,000 receives quarterly deposits of $500 for the first 6 years only. Find the future value of this annuity if it can earn interest at 5% compounded quarterly and the fund matures in 10 years time.

Q16 You presently have $120,000 in an account that earns interest at 6.0% compounded monthly. You will be making end of month deposits of $400 into the account for the next 12 years. How much will you need to deposit at the end of each month for the last 8 years to accumulate $600,000?

Q17 How much money do you need to deposit today so that you can withdraw 12 monthly payments of $400 starting in six months? You can earn 4.8% compounded monthly.

Q18 How much money do you need to deposit today so that you can withdraw 18 monthly payments of $350 starting in four months?  You can earn 9% compounded monthly on your account?

Q19 An endowment fund of $1,500,000 is to pay scholarship grants in perpetuity. The grants are to be paid out semi-annually with the first one to be paid out immediately. If the fund earns interest at 5.5% compounded semi-annually what will be the size of the semi-annual grants?

Q20 Mohawk College has received a donation which is to be used for providing quarterly scholarships. The first quarterly scholarships of $25,000 will be awarded two years and six months from now. If Mohawk College earns interest at 4.25% compounded monthly how much did they receive as a donation?