Your mother helped you start saving £25 a month beginning on your 10th birthday.She always made you make your deposit on the ﬁrst day of each month just to "start the month out right." Today, you turn 21 and have £4,482.66 in your account.What is your rate of return on your savings?

Question

Quizplus · Accepted Answer

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:
A = the ending amount (in this case, £4,482.66)
P = the principal (the amount you initially saved)
r = the annual interest rate (what we're trying to find)
n = the number of times the interest is compounded per year (since it's not specified, we'll assume it's monthly: n = 12)
t = the number of years (from age 10 to age 21, which is 11 years)

We know that you saved £25 per month, which adds up to £300 per year. So your initial principal was:

P = £300 x 12 months x 9 years (from age 10 to age 18) = £32,400

Now we can plug in the values we know and solve for r:

£4,482.66 = £32,400(1 + r/12)^(12*11)
0.138264 = (1 + r/12)^132
ln(0.138264) = 132 ln(1 + r/12)
-1.98076 = 132 ln(1 + r/12)
-0.015 = ln(1 + r/12)
1.015 = 1 + r/12
r/12 = 0.015
r = 0.015 x 12
r = 0.18 or 18%

However, we need to convert this to an annual rate, since we used a monthly n value. To do that, we can use the formula:

APR = (1 + r/n)^n - 1

where APR is the annual percentage rate.

APR = (1 + 0.18/12)^12 - 1
APR = 0.053 or 5.29%

Therefore, the answer is B) 5.29%.

Your Mother Helped You Start Saving £25 a Month Beginning