A politician says that she will give 20 to charity today and

A politician says that she will give $20 to charity today and that she will increase the donation by 10% every day from the previous day. How much does she donate on the 15th day? How much does she donate for 30 days? The donation target is $50000. How many days does it take to reach the target?

Solution

1st day she donates = 20
2nd day she donated = 20*(1.1)
3rd day she donated = 20*(1.1)^2
and so on.....

this is Geometric progression with a = 20 and r = 1.1

a)
an = a*r^(n-1)
a15 = 20*(1.1)^(15-1)
a15 = 20*(1.1)^14
=$75.9
Answer: $75.9

b)
sum of GP,
sn = a (r^n -1) / (r-1)
S30 = 20*(1.1^30 - 1) / (1.1-1)
S30 = 20*(16.45) / (0.1)
=$3290
Answer: $3290

c)
sn = a (r^n -1) / (r-1)
50000 = 20*(1.1^n - 1) / (1.1-1)
(1.1^n - 1) = 250
1.1^n = 251
take log on both sides
log (1.1^n) = log (251)
n*log (1.1) = log (251)
n = 58
She will reach the target on 58th day