Kurt receives a cheque for $38,500 which was the proceeds of an investment (interest plus capital) made 6 months ago at 8.5% p.a. How much did he invest?
Is the answer to this problem $905,882.35?
Thank you to all who can help correct me.
Kurt receives a cheque for $38,500 which was the proceeds of an investment (interest plus capital) made 6 months ago at 8.5% p.a. How much did he invest?
Is the answer to this problem $905,882.35?
Thank you to all who can help correct me.
You haven't said how frequently interest is compounded, so I will assume it is once per year. That's the safest bet if it's not specified... but let me know if you left that information out.
So, assuming simple interest (interest compounded once per year), my calculation is:
x = initial investment amount
x(1+0.085/2) = 38500
x = 38500/1.0425
x = 36,930.46
Does that make sense?
No. In fact, I don't believe the left hand side is equivalent to the right hand side. I think you might be thinking of
$\displaystyle P+I=P(1+r/n)^{nt}$
Or you may have seen it in this form:
$\displaystyle FV=PV(1+r/n)^{nt}$
where r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years the money is invested.
In any case, since we're dealing with simple interest here, that formula won't work for us. We don't want any exponents. This is how I worked through it:
$\displaystyle x$ = initial investment amount
$\displaystyle x(0.085)$ = interest earned over a full year
$\displaystyle x(0.085)/2$ = interest earned over half a year
$\displaystyle x(0.085)/2 + x$ = interest earned over half a year plus principle
$\displaystyle x(0.085)/2 + x = 38,500$
$\displaystyle x(1+0.0425) = 38,500$
$\displaystyle 38,500/1.0425 = 36,930.46$
So I suppose if I had to put that down to a formula that looks like the one you gave, I would write
$\displaystyle FV=PV(1+rm/n)$
where r is the interest rate, m is the number payment periods, and n is the inverse of the fraction of a year during which the money is invested.
Yeah, it's often a problem with people who don't know what they're doing. Tell him (nicely) that the question is grossly incomplete if it doesn't include both the interest rate and the number of compounding periods per year.
I'm going to slightly redefine the terms to make things (hopefully) simplerSo I suppose if I had to put that down to a formula that looks like the one you gave, I would write
$\displaystyle FV=PV(1+rm/n)$
where r is the interest rate, m is the number payment periods, and n is the inverse of the fraction of a year during which the money is invested.
r is the annual interest rate (0.085 in our example)
n is the number of times interest would be paid over the course of a year if the money were left invested for a year or more (2 in our example).
m is the number of potential payment periods during which the money was actually left invested (1 in our example).
Some formulas just say that $\displaystyle I=Prt$, where I is interest, P is principle, r is the rate per period, and t is time. But saying r is the rate per period just means you have to do an extra calculation to find r before plugging it into the formula.