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%.