Question

In: Accounting

You have $5,100 to invest today at 11​% interest compounded annually. Find how much you will have accumulated in the account at the end of

 

FIN101

  1. You have $5,100 to invest today at 11​% interest compounded annually. Find how much you will have accumulated in the account at the end of​: (0.5 Marks each)

(1) 4 years,

(2) 8 years, and​

(3) 12 years.

  1. Using the values​ below, answer the questions that follow:

Amount of annuity

Interest rate

Deposit period​ (years)

 

​$500

9​%

10

  1. Calculate the future value of the​ annuity, assuming that it is
    1. ​An ordinary annuity. (0.5 marks)
    2. ​An annuity due. (0.5 marks)
  1. Compare your findings in parts a​(1) and a​(2). All else being​ identical, which type of annuity—ordinary or annuity due—is preferable as an​ investment? Explain why. (0.5 Marks)

Solutions

Expert Solution

Calculation of Future Value

FV = PV (1+r)n

FV = Future Value

PV = Present Value

r = Interest or discount rate

n = Number of periods or years

(1) FV = $5,100(1+ 0.11)4

FV = $5,100(1.11)4

FV = $7,742.16

(2) FV = $5,100(1+ 0.11)8

FV = $5,100(1.11)8

FV = $11,753.14

(3) FV = $5,100(1+ 0.11)12

FV = $5,100(1.11)12

FV = $17,842.10

Calculation of Future Value of Annuity

Future Value of an Ordinary Annuity

FVOrdinary Annuity  = P X ([1 + I]^N - 1 ) / I

P= Payment Amount

I = Interest (discount) rate

N = Number of payments

FV = $500 X ([1 + 0.09]^10 - 1) / 0.09

FV = $500 X ([1.09]^10 - 1) / 0.09

FV = $7,596.46

Future Value of an Annuity Due

FVAnnuity Due = P X ([1 + I]^N - 1 ) / I X (1 + I)

FV = $500 X ([1 + 0.09]^10 - 1) / 0.09 X (1 + 0.09)

FV = $8,280.15

An Ordinary Annuity is an annuity where cash flows occur at the end of the interest period. An Annuity Due is an annuity where cash flows occur at the beginning of the interest period. As a result, there is one less discounting period for an annuity due, and therefore its present value is higher than an ordinary annuity.

If you're liable for making payments on an annuity, you'll benefit from having an ordinary annuity because it allows you to hold onto your money for a longer amount of time. However, if you're on the receiving end of annuity payments, you'll benefit from having an annuity due, as you'll receive your payment sooner.


Related Solutions

You have $5,100 to invest today at 11​% interest compounded annually. Find how much you will have accumulated in the account at the end of​:
  FIN101 You have $5,100 to invest today at 11​% interest compounded annually. Find how much you will have accumulated in the account at the end of​: (0.5 Marks each) (1) 4 years, (2) 8 years, and​ (3) 12 years. Using the values​ below, answer the questions that follow: Amount of annuity Interest rate Deposit period​ (years)   ​$500 9​% 10 Calculate the future value of the​ annuity, assuming that it is ​An ordinary annuity. (0.5 marks) ​An annuity due....
How much will be in an account at the end of 5 years if you deposit $10,000 today at 8.7% annual interest, compounded semi-annually?
Practice Time Value of Money Problems 1. How much will be in an account at the end of 5 years if you deposit $10,000 today at 8.7% annual interest, compounded semi-annually? 2. What is the balance at the end of 10 years if $2.500 is deposited today and the account earns 4% interest annually? What about if it's quarterly interest? Which one should be more and why? 3. Suppose you want to have $500,000 saved by the time you reach 30 years old....
If you invest $2,000 with a 4% interest rate compounded annually, how much will you have...
If you invest $2,000 with a 4% interest rate compounded annually, how much will you have in ten years? 2-If you are going to receive $2,000 in six years from now, how much is that worth today, assuming 5% annual simple interest? Which of the following options will generate the highest interest over the term, assuming the same $100 principal? Review Later 5% simple interest rate for 3 years 5% quarterly compounding for 3 years 5% monthly compounding for 2...
you deposit $500 today in a savings account that pays 6% interest, compounded annually. How much...
you deposit $500 today in a savings account that pays 6% interest, compounded annually. How much will your account be worth at the end of 40 years?
If you invest $1,000 today into a deposit account earning 5.75% interest compounded monthly, how much...
If you invest $1,000 today into a deposit account earning 5.75% interest compounded monthly, how much would your investment be worth in 10 years?
If you invest $5,000 today into a deposit account earning 6.25% interest compounded monthly, how much...
If you invest $5,000 today into a deposit account earning 6.25% interest compounded monthly, how much would your investment be worth in 5 years?
Q1) Suppose you invest $104,105 today in an account that earns 08.00% interest annually. How much...
Q1) Suppose you invest $104,105 today in an account that earns 08.00% interest annually. How much money will be in your account 10 years from today? Q2) What is the value today, of single payment of $28,298 made 17 years from today, if the value is discounted at a rate of 25.00%? Q3) How many years would it take an investment of $763 to grow to $11,610 at an annual rate of return of 18.00%? Q4) How much money would...
Q1) Suppose you invest $20,958 today in an account that earns 02.00% interest annually. How much...
Q1) Suppose you invest $20,958 today in an account that earns 02.00% interest annually. How much money will be in your account 19 years from today? Q2) What is the value today, of single payment of $6,189 made 12 years from today, if the value is discounted at a rate of 14.00%? Q3) How many years would it take an investment of $264 to grow to $2,845 at an annual rate of return of 08.00%? Q4) How much money would...
You deposit $600 in an account earning 3% interest compounded annually. How much will you have...
You deposit $600 in an account earning 3% interest compounded annually. How much will you have in the account in 15 years?
If you invest $1,632 today and in years 1, 2 and 3 in an account that earns 4.28% APR (compounded annually), how much will you have in the account in 17 years?
 If you invest $1,632 today and in years 1, 2 and 3 in an account that earns 4.28% APR (compounded annually), how much will you have in the account in 17 years?  
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT