Question

how would you solve this on a ba ii plus?

You made an investment of $10,500 into an account that paid you an annual interest rate of 2.2 percent for the first 5 years and 6.6 percent for the next 9 years. What was your annual rate of return over the entire 14 years?

Answer 1

First we will calculate the future value of the investment after 14 years by the following formula:

Here we will use the following formula:

FV = PV * (1 + r1%)n1 (1 + r2)n2

where, FV = Future value, PV = Present value = $10500, r1 = rate of interest for first 5 years = 2.2%, r2 = rate of interest for next 9 years= 6.6%, n1 = time period = 5, n2 = 9

now, putting theses values in the above equation, we get,

FV = $10500 * (1 + 2.2%)5 * (1 + 6.6%)9

FV = $10500 * (1 + 0.022)5 * (1 + 0.066)9

FV = $10500 * (1.022)5 * (1.066)9

FV = $10500 * 1.11494765643 * 1.77752141722

FV = $20809.355

So, the amount at the end of 14 years will be $20809.355

Now, we will calculate the annual rate of return as per below:

FV = PV * (1 + r%)n

where, FV = Future value = $20809.355, PV = Present value = $10500, r = rate of interest , n= time period = 14

now, putting theses values in the above equation, we get,

$20809.355 = $10500 * (1 + r)14

$20809.355 / $10500 = (1 + r)14

1.9818433 = (1 + r)14

(1.9818433)1/14 = 1 + r

1.05 = 1 + r

r = 1.05 - 1

r = 0.05 or 5%

So, annual rate of interest in 14 years is 5%.