What is the required annual interest rate to the nearest tenth of a percent for $5000 to grow to $6200 if interest is compounded quarterly for 8 years.?

1 Answer
Julianna D.
Feb 23, 2018

About 2.7% annually

Explanation:

The equation for compound interest is #A=Pe^(rt)#
#A# is the end number, #P# is the initial price, #e# is a constant, #r# is the rate of change, and #t# is the times it is compounded

Plug it in:
#A=Pe^(rt)#
#6200=5000e^(r(32))#
#6200/5000=e^(r(32))#
#1.24=e^(r(32))#
#log_e(1.24)=r(32)#
#.21511137=r(32)#
#.21511137/32=r#
#r=.00672223#
#r=.672223%#

The rate quarterly is about .7%

The rate yearly is
#.672223(4)#
#2.688892#

About 2.7%

Plug it back in to check:
#6200=5000e^((.02688892/(4))(32))#
#6200=5000e^((.00672223)(32))#
#6200=5000e^(.21511136)#
#6200=5000(1.23999997)#
#6200=6200#

Related questions
Impact of this question
2983 views around the world
You can reuse this answer
Creative Commons License