Answer: I must earn at an annual interest rate of 7.2% over the last 12 years to accomplish the target
Step-by-step explanation:
Firstly, we apply the formula for calculating compound interest :
A = P (1+r)^t
Where A = final amount
P= initial principal balance
r= interest rate
t= time
Since I've just deposited $14,500(initial principal), then rate, r = 7.2% and time, t = 8years. What I seek at this juncture is what the initial deposit will amount to in 8years (That is A). The formula will then be applied and substitution done appropriately.
A = 14,500 × (1+ (7.2/100))^8
A = 14,500 × (1+0.072)^8
A= 14,500 × (1.072)^8
A = 14,500 × 1.744047395
A = $25,288.69
The initial deposit which was $14,500 will amount to $25,288.69 in 8 years at 7.2% annual interest rate.
If the new principal ($25,288.69) must get further to $58,270 in the next 12 years. What will be the annual rate in order for this to be achieved?
We know what A should be ; which is $58,270, current principal = $25288.69, t = 12 years, r = ? (not known).
Applying the same formula and substituting accordingly again, we have:
$58,270 = $25,288.69 × (1 + r)^12
(1 + r)^12 = 58,270/25,288.69
(1 + r)^12 = 2.304192111
1 + r = 12 √2.304192111
1 + r = 1.072037286
r = 1.072037286 - 1
r = 0.072037286
Since rate, r should be in percentage, we multiply "r" by 100
= 0.072037286 × 100
rate = 7.2%
Therefore the interest rate must be 7.2% and I have to earn at this rate over the last 12 years to get my money to $58,270