a kind benefactor sets up a prize in an international school. the benefactor donates $10 000. the school invests the money in an account paying 5% interest. if $750 was paid out annually, for how long can the full prize be given out?
2+2=5
Tf, 1 cig= Anze
The present value An of the annuity=10,000
An=p*(1-(1+i)^-n)/i
10000=750*(1-1.05^-n)/0.05
500=750*(1-1.05^-n)
2/3=1-1.05^-n
1.05^-n=1/3
1.05^n=3
n=ln3/ln1.05=22.51708531
its quite easy to do check slapni
To determine how long the full prize can be given out, we need to calculate the time it takes for the interest earned on the investment to reach $10,000.
Let's break down the problem step by step:
1. First, we need to calculate the annual interest earned on the investment. The investment amount is $10,000, and the interest rate is 5%. To find the annual interest, we can multiply the investment amount by the interest rate:
Annual Interest = $10,000 * 5% = $500
2. Next, we need to determine how many times the annual interest needs to be paid out to reach the full prize amount of $10,000. We know that $750 is paid out annually, so we can divide the annual interest by the annual payout:
Number of Payouts = $500 / $750 = 2/3
3. Since we can't have a fractional number of payouts, we need to round down to the nearest whole number. In this case, rounding down means no payouts will be made in the final year. Therefore, we can conclude that the full prize can be given out for 2 years.
Therefore, the full prize can be given out for a duration of 2 years.