Question

a capital of 500 dollars earns 150 dollars of interest in 6 years. What was the

interest rate if compound interest is used? What if simple interest is used?

Answer 1

Compound interest

$A = P(1 +\frac{ r}{n})^{nt}$

A=final amount

P=initial principal balance

r=interest rate

n=number of times interest applied per time period

t=number of time periods elapsed

Amount=Interest+Amount

$=150+500=650$

$A = P(1 +\frac{ r}{n})^{nt}$

$650 = 500(1 +\frac{ r}{1})^{1×6}$

$1.3=(1+r)^6$

$\sqrt[6]{1.3}=1+r\\=1.0446750$

$1.0446750-1=0.0446750\\4.46750\%$

Simple interest

$I=P×I×T$

• P = Principal Amount
• I = Interest Amount
• r = Rate of Interest per year in

$150=500×I×6\\150=3000I\\I=0.05\\0.05×100=5\%$