Problem 21 2 points What is the effective interest rate for

Problem 2-1 (2 points) What is the effective interest rate for an advertised rate of 8% compounded quarterly? Problem 2-2 (2 points) How much would you need to invest at 6% interest on December 31, 2013, in order to accumulate S1850 on December 31, 2021? Present the economic functions required, showing the functional notation and then its numerical value.

Solution

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\"The effective annual interest rate is the interest rate that is actually earned or paid on an investment, loan or other financial product due to the result of compounding over a given time period. It is also called the effective interest rate, the effective rate or the annual equivalent rate.

So if nominal interest rate (i), number of compounding in a year is (m), effective interest will be

Effective interest rate = (1 + i/m) ^m -1

Where,

Nominal interest rate (i) = 0.08 per year

Number of compounding in a year (m) = 4

Let’s put all the values in the formula

Effective interest rate = ( 1 + 0.08/4) ^4 - 1

                                              = ( 1 + 0.02) ^4 - 1

                                              = ( 1.02) ^4 - 1

                                              = 1.08243 - 1

                                              = 0.08243

So annual effective interest rate is 8.24% per year

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Present value is the present worth of cash that is to be received in the future, if future value is known, rate of interest in r and time is n then PV is

PV = FV/ (1 + r) ^n

Where,

FV = 1850

r = 0.06

n = 8

Let\'s put all the values in the formula

= 1850/ (1 + 0.06)^8

= 1850/ (1.06)^8

= 1850/ 1.5938

= 1160.75

So PV of 1850 after 8 years is 1160.75

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Hope that helps.

Feel free to comment if you need further assistance J