You have just deposited $14,500 into an account that promises to pay you an annual interest rate of 7.2 percent each year for the next 8 years. You will leave the money invested in the account and 20 years from today, you need to have $58,270 in the account. What annual interest rate must you earn over the last 12 years to accomplish this goal

Answer: I must earn at an annual interest rate of 7.2% over the last 12 years to accomplish the target

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