Question

* Engineering Economic Analysis

How much money must be invested in an account that pays 6% per year in- terest to be worth $20,000 at the end of 8 years if (forgetting leap years and making “convenient” assumptions):

(a) Interest is compounded annually ?

(b) Interest is compounded semi-annually ?

(c) Interest is compounded quarterly ?

On (c), provide the solutions using the Compound interest table AND the formula AND the EAIR

Answer 1

How much money must be invested in an account that pays 6% per year in- terest to be worth $20,000 at the end of 8 years if (forgetting leap years and making “convenient” assumptions):

(a) Interest is compounded annually ?

(b) Interest is compounded semi-annually ?

(c) Interest is compounded quarterly ?

a) Effective annual rate of interest = 6%. Amount to be invested now = 20000(P/F, 6%, 8) = 20000*0.6274 = 12,548

b) Effective semi-annual rate of interest = (1 + 6%/2)^2 -1 = 6.09%. Amount to be invested now = 20000(P/F, 6.09%, 8) = 20000*0.6232 = $12,464

c) Effective annual interest rate = (1 + 6%/4)^4 - 1 = 6.136%. Amount to be invested now = 20000(P/F, 6.136%, 8) = 20000*0.6210 = $12,420