Answer:
$17,256.9
Explanation:
Compound interest : This is the interest earned on both the principal amount plus any already earned interest i.e the compound amount.
Under the compound interest, interest for a period is computed by multiplying the interest rate by the principal amount plus already earned interest. This will will done weekly, if the interest rate is qouted to be compounded weekly
For example, if an investment promises 5% per annum and I invested $1000 for 2 years. My interest is computed as follows:
Interest earned per year will be as follows:
Year 1 = 5% × $1000= $50
Year 2= (5% ×1000) + (5% ×$50)= $52.50
Total interest = $102.50
The total worth of the investment after the the investment period is called the Future Value i.e the principal + interest earned
Using my example, my future value will be
FV = 1000 + 120.50 = $1,102.5
The amount invested today or borrowed is called the Present value/principal
A shorter way to compute the future value is :
FV=PV × ( (1+r/m)^(n×m) )
r= interest rate, m = number compounding period in a year, n =number of year, PV = ?
So we can apply this formula as follows to our question:
Note that the interest rate is quoted per week, so we do not have do divide the rate by the number of weeks.
29,500 = PV × (1+0.00172)^(6 ×52)
29,500 = PV × 1.70946
PV = 29,500/1.70946
PV = $17,256.9
