What is the rate of annual interest?

Question

If John inherited $200000 and wanted it to grow into &500000 in 25 years, what rate of annual interest compounded monthly would he need to earn to reach his goal? Solve this problem algebraically.

 

AWNSER: r=3.67%

 

im am not able to find how to do it. 

Answer 1

We use the compound interest formula

 

A = P(1 + (r/n))^nt

 

where:

A = money accumulated

P = investment

r = interest rate (in decimal form)

t = time

n = number of times compounder per year

 

P = 200000

A = 500000

t = 25

n = 12

 

First, lets solve for r by manipulating the formula.  Then plug in the numbers.

 

A = P(1 + (r/n))^nt

 

 

Divide both sides of equation by P.

 

A/P = (1 + (r/n))^nt

 

 

Raise both sides of the equation by the power of 1/(nt).  This is equivalent to the nt -root.

 

^nt√(A/P) = 1 + r/n

 

 

Subtract 1 on both sides of equation.

 

( ^nt√(A/P)) - 1 = r/n

 

 

Multiply both sides of equation by n.  Then multiply by 100.

 

n[(^nt√(A/P)) - 1] * 100 = r

 

100n[(^nt√(A/P)) - 1] = r