a) Using the formula T = P(1 + RN), where P is the principal, R is the annual interest rate, N is the number of years, and T is the total amount including simple interest:
T = $30,000(1 + 0.07 × 10)
T = $30,000(1.7)
T = $51,000
Therefore, the total amount after 10 years if $30,000 is invested at 7% p.a. is $51,000.
b) Using the same formula, we can solve for the number of years (N) needed for an investment of $18,000 to grow to $22,320 at 6% p.a. simple interest:
$22,320 = $18,000(1 + 0.06N)
1.24 = 1 + 0.06N
0.24 = 0.06N
N = 4
Therefore, it takes 4 years for an investment of $18,000 to grow to $22,320 at 6% p.a. simple interest.