Kiran is a die-hard Apple fan and he wants to get the new iPhone 12 after it is released at an expected cost of $1,849. He currently has $1,356 saved with St George Bank in a special savings account earning 16% p.a. compounding weekly. How many weeks must Kiran wait until she has enough money to get the new iPhone?

To solve this problem, we need to use the formula for compound interest, which is:

A = P(1 + r/n)^(nt)

Where: A = the amount of money accumulated after n years, including interest. P = the principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = the time the money is invested for in years

In this case, we need to solve for t (time), so we will rearrange the formula to solve for t:

t = log(A/P) / (n * log(1 + r/n))

Given: P = $1,356 (the amount Kiran currently has) A =$1,849 (the amount Kiran needs to buy the iPhone) r = 16% p.a. = 0.16 (annual interest rate in decimal) n = 52 (since the interest is compounded weekly)

Substituting these values into the formula:

t = log(1849/1356) / (52 * log(1 + 0.16/52))

First, calculate the values inside the log functions:

log(1849/1356) = log(1.36342) = 0.13499 (rounded to 5 decimal places) log(1 + 0.16/52) = log(1.003076923) = 0.00136 (rounded to 5 decimal places)

Then substitute these values back into the formula:

t = 0.13499 / (52 * 0.00136) = 0.13499 / 0.07072 = 1.908 (rounded to 3 decimal places)

Since t is in years, we need to convert it to weeks (since the question asks for the number of weeks). There are 52 weeks in a year, so:

t (in weeks) = 1.908 * 52 = 99.216 weeks

So, Kiran needs to wait approximately 100 weeks (rounding up to the nearest whole number, since you can't wait a fraction of a week) to have enough money to buy the new iPhone.