Calculating Present Value: $50 U.S. Savings Bond at 6.22% Compounded Monthly

[DCHomage]

Homework Statement

A $50 U.S. Savings Bond paying 6.22% compounded monthly matures in 11 years 2 months. What is the present value of the bond?

Homework Equations

The Attempt at a Solution

I ended up getting $50.95

 

[Mark44]

Homework Statement

A $50 U.S. Savings Bond paying 6.22% compounded monthly matures in 11 years 2 months. What is the present value of the bond?

Homework Equations

The Attempt at a Solution

I ended up getting $50.95

That's not a reasonable answer. No reasonable person would pay $50.95 now for a bond whose value is $50 at maturity, which is 11 years 2 months in the future.

The idea is that you pay a smaller value in the present and get a larger value in the future. Surely you must have an equation that you can use.

 

[DCHomage]

That's not a reasonable answer. No reasonable person would pay $50.95 now for a bond whose value is $50 at maturity, which is 11 years 2 months in the future.

The idea is that you pay a smaller value in the present and get a larger value in the future. Surely you must have an equation that you can use.

The compound interest formula?

 

[Mark44]

Sure. Give it a whirl and show us your work.

 

[DCHomage]

Sure. Give it a whirl and show us your work.

I did 50(1+(0.0622/12))^(12/11.167) so...is the answer $99.96?

 

[HallsofIvy]

You are going the wrong way! That would be the return if you invested $50. With a $50 bond,you get $50 on maturity. How much would invest (the principal) at 6.22% interest, for 11 years 2 months, to get a return of $50? (it will be less than $50.)

Also the number of months in 11 years 2 months is 11.167 times 12, not divided by 12.

 

[symbolipoint]

Try going to a lower level. You know the compounding is monthly; so how many months does the bond earn? This is 6.22 % each month; and the interest is COMPOUNDED monthly.

 

[HallsofIvy]

Try going to a lower level. You know the compounding is monthly; so how many months does the bond earn? This is 6.22 % each month; and the interest is COMPOUNDED monthly.

No, the interest is NOT 6.22% each month. The problems says "A $50 U.S. Savings Bond paying 6.22% compounded monthly". While it is compounded monthly, the interest rate stated is, as always, annual interest.

Even the United States Government isn't stupid enough to pay 12(6.22)= 74.64% annually!

 

[DCHomage]

My bad...I did 50/(1+(0.0622/12))^(-12x11.167). That how I ended up with 99.96.

 

[DCHomage]

Is it 99.96 or not?

 

[Mark44]

NOT. Please reread (or maybe read) what Halls and I have written. It should be a clue when you ask whether $99.96 is correct and someone replies that you're going the wrong way.

 

[DCHomage]

I used the compound interest formula and ended up with that so what did I do WRONG?

 

[Mark44]

Carefully read Halls's post #6.