We can use the formula for compound interest to solve this problem:
A = P(1 + r/n)^(nt)
where:
A = the final amount
P = the principal amount (the initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, A = $138,000, r = 0.053 (5.3% as a decimal), n = 365 (daily compounding), and t = 12.
So we can plug in these values and solve for P:
$138,000 = P(1 + 0.053/365)^(365*12)
$138,000 = P(1.0053)^4380
P = $138,000 / (1.0053)^4380
P ≈ $59,073
So Kiran would need to invest approximately $59,073, rounded to the nearest dollar, for the value of the account to reach $138,000 in 12 years with daily compounding at a 5.3% interest rate.