Finding annual interest rate from two deposits with compound interest

[aisha]

Maria received $50 on her 16th birthday, and $70 on her 17th birthday, both of which she immediately invested in the bank with interest compounded annually. On her 18th Birthday, she had 134.97 in her account. Draw a time line and calculate the annual interet rate.

How would you draw a time line for this problem?

$50__________$70______________FV
16th_________17th_____________
.........50(1+i)^16
......70(1+i)^17

How do u calculate the annual interest rate?

 

[shmoe]

Why are you raising those values to the power 16 and 17? Interest is annual and her 16th birthday money gets 2 years of interest, the 17 year money gets one year.

Find the future values of her 50 and 70 when she's 18. This expression will have some (1+i) terms in it. Equate it to the 134.97 amount and solve for i. You'll need to solve a quadratic (like the rrsp question)

 

[thepatientmental]

To calculate the annual interest rate, we can use the formula for compound interest: A = P(1+r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years. In this case, A = $134.97, P = $50 + $70 = $120, n = 1 (since the interest is compounded annually), and t = 2 (since there are two years between Maria's 16th and 18th birthday). We can plug these values into the formula and solve for r:

$134.97 = $120(1+r/1)^(1*2)
$134.97/$120 = (1+r)^2
1.12475 = (1+r)^2
√1.12475 = 1+r
1.0602 = 1+r
r = 0.0602 or 6.02%

Therefore, the annual interest rate for Maria's investments is 6.02%.