Bryan invests $500 in an account earning 4% interest that compounds annually. If he makes no additional deposits or withdraws, how much will be in the account:
About how long would it take to double his $500 investment? Round to one decimal place.
no time given for the first part.
2nd part:
500(1.04)^n = 1000
1.04^n = 2
take log of both sides
n log 1.04 = log 2
n = log2/log1.04 = 17.67 years
or n = 17.7 years correct to one decimal
To determine how long it would take for Bryan's $500 investment to double, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment (the amount in the account)
P = the principal (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case, the principal (P) is $500, the annual interest rate (r) is 4% or 0.04, and since the interest is compounded annually, n = 1.
We can rewrite the formula as:
A = 500(1 + 0.04/1)^(1t)
To find out when the investment will double, we need to solve for t. So we set A equal to 1000 (double the initial investment):
1000 = 500(1 + 0.04)^t
Dividing both sides of the equation by 500:
2 = 1.04^t
Taking the natural log (ln) of both sides of the equation to solve for t:
ln(2) = ln(1.04^t)
Using the property of logarithms, we can bring down the exponent:
ln(2) = t * ln(1.04)
Finally, divide ln(2) by ln(1.04) to solve for t:
t = ln(2) / ln(1.04)
Using a calculator, we can compute this value:
t ≈ 17.7
Rounded to one decimal place, it would take approximately 17.7 years for Bryan's $500 investment to double at an annual interest rate of 4% compounding annually.