1. ## money and interest

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

2. sorry thats ment to say and not nad

3. so P(1 + R)^t = 2P?

lemme see.

(1 + R)^10 = 2

R = 10.root(2) - 1
Thus R = 7.18% approx.

4. 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