Joseph R. answered • 12/14/21
Patient and experienced tutor specializing in math & science.
First, write the Compound Interest Formula
A = P(1+r/n)nt
A = Amount
P = Principle
r = Interest Rate (decimal)
n= number of times interest is compounded per unit 't'
t = Time
To calculate how long the principle will double from $5,000 to $10,000 using simple interest of 7.4% APR:
A = P(1+r/n)nt
Plug the given values into the formula (n = 1 if interest is compounded once a year; n = 12 if interest is compounded monthly; n = 365 if interest is compounded daily)
10,000 = 5,000 * (1 + 0.074/1)1*t
10,000/5,000 = (1 + 0.074)t
2 = 1.074t
ln(2) = ln(1.074t)
ln(2) = t*ln(1.074)
0.6931 = t * 0.0714
0.6931 / 0.0714 = t
9.71 = t; the principle would double in 9.71 years if interest is compounded yearly
To solve for monthly and daily compound interest, change variable 'n'.
How much money would be in the account after 10 years (compounded monthly) for each of the following investments. Round to the cent.
A = P(1+r/n)nt
A = 5,000 * (1 + .074/12)12*10
A = 10,455.89
To solve for monthly and daily compound interest, change variable 'n'.
Joseph R.
Yes, well done! As the frequency of compounding increases, it takes less time for the principal (5,000) to double.12/15/21
Autumn N.
Thank you so much! I’d like to double check my understanding with you on the first half of the problem. Would the monthly compound take 9.39 years and the daily compound take 9.37 years?12/15/21