Calculating Value of Investment: $5,000 at 6.3% Interest

[hostergaard]

a sum of $ 5 000 is invested at a compound interest rate of 6,3% per annum.
the value of the investmen vill exceed $ 10 000 after n full years.
(a) write an inewuality to represent this information.
(b) calculate the minimum value of n.

please help. english is my second langue and I am a bit confused

 

[praharmitra]

you need to use the equation for compound interest rates. This is, as u probably know
$$A = P(1+\frac{R}{100})^n$$

You are given P, R and the required minimum value of A. You are to find the minimum value of n

 

[Architeuthis Dux]

(a) The value of the investment, V, will exceed $10,000 after n full years, where V > $10,000.
(b) To calculate the minimum value of n, we can use the compound interest formula: V = P(1+r)^n, where P is the initial investment, r is the interest rate, and n is the number of years. Plugging in the given values, we get:
$10,000 = $5,000(1+0.063)^n
$2 = (1.063)^n
Taking the logarithm of both sides, we get:
log($2) = n*log(1.063)
n = log($2)/log(1.063)
n ≈ 11.56
Therefore, the minimum value of n is 12 years.