Sherpa invests $10,000 in a saving account which pays a compound interest at R% per year if the total interest earned in 2years is $400, find the value of R.

Solve this for R (as a decimal):

10,000*(1 + R)^2 = 10,400
(1+R)^2 = 1.0400
1+R = 1.0198
R = 0.0198 or 1.98%

To find the value of R, we can use the compound interest formula:

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

Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years

In this case, Sherpa invests $10,000, the total interest earned after 2 years is $400. We need to find the value of R, which represents the annual interest rate.

Let's substitute the given values into the formula:

A = P(1 + r/n)^(nt)
$10,400 = $10,000(1 + r/n)^(2n)

Now, we need to solve for R. To simplify the equation, let's divide both sides by $10,000:

$10,400/$10,000 = (1 + r/n)^(2n)

Simplifying further:

1.04 = (1 + r/n)^(2n)

Now, we can solve for R by using trial and error or by using logarithms.

Let's use trial and error to find the value of R:

Assume n = 1 (compounded annually):
1.04 = (1 + r/1)^(2*1)

1.04 = (1 + r)^2

Taking the square root of both sides:
√1.04 = 1 + r

Simplifying:
1.019 = 1 + r

Subtracting 1 from both sides:
0.019 = r

R = 0.019, or 1.9%

Therefore, the annual interest rate R is 1.9%.