sorry thats ment to say and not nad
the question says" when an amount is invested and compounded monthly, the amount is doubled after 10 years"
a) identify a case where this would be true. stipulate the principle nad rate. prove.
b) "this case is only true for one interest rate." explain mathematically if the statement is valid
thank you for all your help i need it this arfternoon if possible thank you
xxx
Hello, mini!
When an amount is invested and compounded monthly,
the amount is doubled after 10 years.
a) Identify a case where this would be true.
Stipulate the principle and rate. .Prove.
b) "This case is only true for one interest rate."
Explain mathematically if the statement is valid.
Use the compound interest formula: .A .= .P(1 + i)^n
where: P = the principal invested
. . . . . .i = periodic interest rate
. . . . . n = the number of periods
. . . . . A = the final amount of the investment
We have P dollars invested at i percent per month for 120 months
. . and its value grows to 2P.
So we have: .P(1 + i)^120 .= .2P . . → . . (1 + i)^120 .= .2
Take the 120th root of both sides: .1 + i .= .(2)^1/120 .= .1.005792941
Then: .i .= .0.005792941 .(monthly interest rate)
Therefore, the annual interest rate is: .12 × 0.005792941 .= .0.069515293
. . or about 7%.
This is the only interest rate which satisfies the problem.
. . (Note that the Principal does not matter.)