This exercise is based on the following table, which lists interest rates on long-term investments (based on 10-year government bonds) in several countries in 2008.
Assuming that you invest $12,000 in the Japan(1.5%), how long (to the nearest year) must you wait before your investment is worth $16,000 if the interest is compounded annually?
What formula do I use to solve this and how? I got 17 years but its wrong
thank you
See 2-29,3:41am post.
To solve this problem, you need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the initial principal amount (in this case, $12,000)
r = the annual interest rate as a decimal (in this case, 1.5% or 0.015)
n = the number of times interest is compounded per year (since it is compounded annually, n would be 1)
t = the number of years
In this case, you want to find the value of t (the number of years) when the investment is worth $16,000. So the equation becomes:
$16,000 = $12,000(1 + 0.015/1)^(1t)
To solve for t, we need to isolate it. First, divide both sides of the equation by $12,000:
$16,000/$12,000 = (1 + 0.015)^(1t)
Cancel out the denominators:
4/3 = (1 + 0.015)^t
Now, take the logarithm of both sides to solve for t:
log(4/3) = log((1 + 0.015)^t)
Using the logarithm properties, we can bring the exponent down:
log(4/3) = t * log(1 + 0.015)
Finally, divide both sides by log(1 + 0.015):
t = log(4/3) / log(1 + 0.015)
Using a calculator to evaluate this expression, we find that t is approximately 77.92. However, since we are looking for the answer in years, we round it to the nearest whole number.
Therefore, you need to wait approximately 78 years (to the nearest year) before your investment is worth $16,000 if the interest is compounded annually in Japan.