Zoey has invested $30 000 in a registered education savings plan (RESP). She wants her investment to grow to at least $50 000, so that her newborn can go to university at age 18. What interest rate, compounded annually, will result in a future value of $50 000? Round to the nearest tenth of a percent.
To find the interest rate, compounded annually, that will result in a future value of $50,000, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the initial investment amount
r = the interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case, Zoey has invested $30,000 (P), and wants the investment to grow to $50,000 (A) over time. We can assume that n is 1 (annual compounding) and t is 18 years.
Using the formula, we can rearrange it to solve for r:
r = ( (A / P)^(1/(n*t)) ) - 1
Plugging in the values:
r = ( ($50,000 / $30,000)^(1/(1 * 18)) ) - 1
r = (1.6667^(1/18)) - 1
Calculating this in a calculator or spreadsheet:
r ≈ 0.0745
Therefore, the interest rate, compounded annually, that will result in a future value of $50,000 is approximately 7.5% (rounded to the nearest tenth of a percent).
50000 = 30000 (1 + i)^18
log(5/3) = 18 log(1 + i)
.012325 = log(1 + i)