Question

peter needs a care in about 5 years and believes he'll need about $15,000.00 and plans on depositing his money into an account with a 12% interest rate compounded semiannually. how much does Pete need to deposit?

Answer 1

Compound interest formula:
\[Final=Initial(1+i)^{2n}\]
Note: It is 2n because it is compounded twice anually.
Final is 15,000, i is 0.12, and n is 5. Substituting gives us the equation:
\[15000=Initial(1.12)^10\]
Dividing through by \((1.12)^{10}\) gives:
\[Initial=4829.6\]
Does that make sense or would you like me to explain something more?