Question

Example 8: (CC5e p. 63) Consider two investment offers: an APR of 6.9% compounded quarterly (Investment A) or an APR of 6.7% compounded monthly (Investment B). a. Determine the better investment by calculating the effective rate (APY) for each. • Investment A • Investment B b. Compare the time it will take an investment to double for each offer. Which investment doubles more quickly and is therefore the better investment? • Investment A • Investment B

Answer 1

Solution:
(a) Effective rate:
*Investment A
➡ Compound interest formula
=[(1+(r/n))^n] -1
r= rare of interest
n= number of times interest compounded

Investment A is compounded quarterly(4 times) at 6.9%
   =[(1+(r/n))^n]-1
   =[(1+(0.069/4))^4]-1
   =[(1+0.01725)^4]-1
   =[(1.01725)^4]-1
   =(1.070806) - 1
   =0.070806
   =7.0806%

*Investment B
Investment B is compounded monthly (12 times) at 6.7%
   =[(1+(r/n))^n]-1
   =[(1+(0.067/12))^12]-1
   =[(1+0.005583)^12]-1
   =[(1.005583)^12]-1
   =(1.06909) - 1
   =0.069091
   =6.9091%

(b) Time required for making the investment double :

*Rule of 72:
➡ 72 divided by the rate of interest
Investment A= 72/7.0806 = 10.16 years
Investment B = 72/6.9091 = 10.42 years

Investment A requires less time, hence it should be considered.