1.
Kevin borrowed $2000 from his mother at an interest rate of 5%, compounded monthly. How much does he owe (including the original $2000) at the end of 3 years? Give your answer rounded to the nearest cent.
2.
Five thousand dollars compounded annually at an \(x\% \) interest rate takes six years to double. At the same interest rate, how many years will it take \($300\) to grow to \($9600\)?
+532 1)
3 years is 36 months, so the amount he owes is 2000 dollars * (1 + 5%) ^ 36, which, using a calculator, is approximately 11583.63.
2)
We are given that it takes 6 years to double. Because the same percentage applies with the same properties, after 6 years, the 300 dollars turns into 600, then 1200, then 2400, then 4800, then 9600. This doubles 5 times, which is 5 * 6 = 30 years.
1 - FV = PV x [1 + R]^N
FV =2,000 x [1 + 0.05/12]^(3*12)
FV =2,000 x [1.0041666667]^36
FV =2,000 x [1.1614722313....]
FV = $2,322.94 - what Kevin owes his mother after 3 years @ 5% comp.monthly.
2 - FV = PV[1 + R]^N
$2=$1[1 + R]^6 - Take the 6th root of both sides
R =~12.25%
9,600 = 300 x 1.1225^N Divide both sides by 300
32 = 1.1225^N Take the log of both sides
N = log(32) / log(1.1225)
N =~30 - years for $300 to grow to $9,600
