Plz answer this mathematics question with complete calculating steps plz.thx?

Question

(a)When Charles's first child, John is born, Charles invested RM300 for him at 8% compound interest per annum. He continues to invest RM300 on each of John's birthday, up to and including his 18th birthday.What will be the total values of the investment on John's 18th birthday?

(b)If Charles starts his investment with RM500 instead of RM300 at the same interest rate, calculate on which birthday will the total investment be more than RM25000 for the first time.

RM can be said as $

the answer for the question (a) is RM1198.79 an d the answer for (b) is RM25171.42.i juz need the steps of calculations now.

Answer 1

This is an annuity investment, and can be represented as the sum of a geometric series:
A = p((1 + i)^n - 1) / ((1 + i) - 1) = p((1 + i)^n - 1) / i
A = 300(1.08^18) - 1) / 0.08
A = RM 11,235.07

(b)
25,000 = 500(1.08^n) - 1) / 0.08
500(1.08^n - 1) = 0.08(25,000)
1.08^n - 1 = 0.08(25,000) / 500
1.08^n = 1 + 0.08(25,000) / 500
nln(1.08) = ln(1 + 0.08(25,000) / 500)
n = ln(1 + 0.08(25,000) / 500) / ln(1.08)
n = 20.91237
For A > RM 25,000, n = 21

Answer 2

P = C (1 + r) t
where
P = future value
C = initial deposit
r = interest rate (expressed as a fraction: eg. 0.06)
n = # of times per year interest in compounded
t = number of years invested

(a) P = C (1 + r) t
P = 300(1 + .08)18
P = 300(1.08)18
P = $5832

(b) 25000 = 500(1 + .08)t
25000 = 500(1.08)t
25000 = 540t
25000/540 = (540/540)t
46.30 = t --> on his 47th birthday the total investment will be more than $25000 for the first time

Answer 3

a) T(1) = 300
T(2) = 300*1.08 + 300
T(3) = (300*1.08 + 300)*1.08 + 300
= 300*(1.08^2) + 300*1.08 + 300

which is equivalent to summation of geometric sequence S(n) is where a = 300, r = 1.08.

So
S(18) = 300 (1.08^18-1)/(1.08-1) = 11235

b) S(n) > 25000, with a = 500

500 (1.08^n)/(1.08-1) > 25000
1.08^n > 50*0.08
1.08^n > 4
n lg 1.08 > lg 4
n > 0.6021/0.0334
n > 18.01

On year of 19th, the amount would exceed RM 25000

Answer 4

a) you have to do it step by step..every year
108% times RM300 = RM324
2nd year
108% times RM624 = ............