logo for solving-math-problems.com
leftimage for solving-math-problems.com

Compound Interest: 5% compounded quarterly for the first 2 years …











































RM10000 is invested for 5 years. The investment offers an interest of 5% compounded quarterly for the first 2 years and 6 months and 8% compounded monthly for the rest of the period. Find

i)The future value of this investment
ii) The total interest earned
iii) The effective rate that is equivalent to 5% compounded monthly


Comments for Compound Interest: 5% compounded quarterly for the first 2 years …

Click here to add your own comments

Jul 27, 2011
Compound Interest
by: Staff

-----------------------------------------------

Part II


ii) The total interest earned

Total interest earned = RM 13820.4 - RM 10000

Total interest earned (over the entire 5 year period) = RM 3820.4


iii) The effective rate that is equivalent to 5% compounded monthly

The interest rates provided in the statement of this problem are called Nominal Interest Rates. 5% compounded quarterly and 8% compounded monthly are Nominal Interest Rates. A Nominal Interest Rate is also called the "Stated Rate" or the APR (annual percentage rate).

The Effective Interest Rate is the actual interest rate. It is also called the APY (annual percentage yield).

The Effective Interest Rate can be calculated as follows:

Effective Interest Rate = (1 + i/n)ⁿ - 1

i = the nominal interest rate in decimal form
n = number of compounding periods used during 1 year

(This is the essentially the same formula we used in part i) to compute the interest earned on the investment of RM10000.)

The effective rate that is equivalent to 5% compounded monthly

Effective Interest Rate = (1 + i/n)ⁿ - 1

i = .05
n = 12 months

Effective Interest Rate = (1 + .05/12)¹² - 1

Effective Interest Rate = (1 + 0.00416667)¹² - 1

Effective Interest Rate = (1.00416667)¹² - 1

Effective Interest Rate = 1.05116 - 1

Effective Interest Rate = .05116

Effective Interest Rate as a % = .05116 * 100


Effective Interest Rate = 5.116 %



The final answers are:


i)The future value of this investment

after 2 ½ years, value = RM 11322.7

after 5 years, value = RM 13820.4


ii) The total interest earned

Total interest earned (over the entire 5 year period) = RM 3820.4


iii) The effective rate that is equivalent to 5% compounded monthly

Effective Interest Rate = 5.116 %


Thanks for writing.

Staff
www.solving-math-problems.com



Jul 27, 2011
Compound Interest
by: Staff


Part I

The question:

RM10000 is invested for 5 years. The investment offers an interest of 5% compounded quarterly for the first 2 years and 6 months and 8% compounded monthly for the rest of the period. Find

i)The future value of this investment
ii) The total interest earned
iii) The effective rate that is equivalent to 5% compounded monthly


The answer:

i)The future value of this investment

5% compounded quarterly for the first 2 ½ years

A = P*(1 + r)^t

A = final balance of the investment after the first 2 ½ years
P = principle (the initial investment)
r = decimal form of quarterly interest rate
t = time in quarters

P = RM10000
r = 0.0125 (.05 is the decimal form of 5%. It is = 5÷100. r = the quarterly interest rate: .05/4 = 0.0125)
t = 10 quarters


A (at 2 ½ years) = P*(1 + r)^t

A (at 2 ½ years) = 10000*(1 + 0.0125)^10

A (at 2 ½ years) = 10000*(1.0125)^10

A (at 2 ½ years) = 10000*(1.132271)

A (at 2 ½ years) = RM 11322.71


8% compounded monthly for 2 ½ years

A = P*(1 + r)^t

A = final balance of the investment after 5 years
P = principle (the final value of the investment after the first 2 ½ years)
r = decimal form of monthly interest rate
t = time in months

P = RM 11322.7
r = 0.00666667 (.08 is the decimal form of 8%. It is = 8÷100. r = the monthly interest rate: .08/12 = 0.00666667)
t = 30 months


A (at 5 years) = P*(1 + r)^t

A (at 5 years) = 11322.7*(1 + 0.00666667)^30

A (at 5 years) = 11322.7*(1.00666667)^30

A (at 5 years) = 11322.7*( 1.22059)

A (at 5 years) = RM 13820.4

-----------------------------------------------

Click here to add your own comments

Join in and write your own page! It's easy to do. How? Simply click here to return to Math Questions & Comments - 01.



Copyright © 2008-2015. All rights reserved. Solving-Math-Problems.com