Question

What principle will amount to $1000 if invested at 3% compounded quarterly for 9 years? The Principle was $

Answer 1

P=$764.18

Explanation:

Compounding Formula:
`A = P(1+(r)/(n)) ^(nt)`

We can start with putting the numbers in sections:

A = Final Amount ($1,000)

P = Initial Principle Balance (*We are trying to find)

R = Interest Rate (3%)

N = Number of times per year (Quarterly/4)

T = Over how much time (9)

Now put them in the formula
`1000 = P(1+(.03)/(4)) ^(((4)(9)))`

Now to solve for P...

• Start with Parenthesis (4)(9) = 36
• Now you have
  `1000 = P(1+(.03)/(4)) ^(36)`
• Simplify
  `(1+(.03)/(4))` to 1.0075 (when doing this start with division)
• Now you have
  `1000 = P(1.0075) ^(36)`
• Simplify
  `(1.0075)^(36)` which = 1.3086

• Now you have
  `1000 = P(1.3086)`
• Now divide 1.3086 on both sides. 1000/1.3086 = 764.175
• Now you have 764.175 = P

Rounding up your answer should be $764.18