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
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