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Question 350478: The U.S. Treasury offers to sell you a bond for $613.81 no payments will be made until the bond matures 10 years from now at which time it will be redeemed for $1,000. What interest rate would you earn if you bought this bond at the offer price
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! You pay $613.81 for the bond.
You get $1,000 back in 10 years.
With annual compounding, your money has earned 5.001766149% per year.
The yearly increase in the investment is shown below:
YEAR BALANCE
0 $613.81
1 $644.51
2 $676.75
3 $710.60
4 $746.14
5 $783.46
6 $822.65
7 $863.79
8 $907.00
9 $952.36
10 $1,000.00
You start off with 613.81.
You multiply that by 1.05001766149 each year for 10 years and wind up with $1,000 at the end of it.
The factor 1.05001766149 is derived as follows:
5.001766149% divided by 100% = .05001766149
That's the interest rate per year.
The value of the investment in the next year is equal to the investment in that year + the investment in that year times the interest rate.
That would be 613.81 + 613.81 * .05001766149
You take out the common factor in this to get:
613.81 * (1 + .05001766149) which becomes:
613.81 * 1.05001766149.
That's the growth in the first year.
With compounding, the same formula is applied to the new value in the next year, and the next year, and the next year, up until you reach year 10.
The money you receive from the bond in 10 years is equivalent to investing the $613.81 in an account that is paying you 5.001766149% per year compounded annually.
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