Interest Math Problem?

Question

Tanya has just inherited a diamond ring appraised at $3500. If diamonds have appreciated in value at an annual rate of 8%, what was the value of the ring 10 years ago when the ring was purchased? Give your answer correct to the nearest cent.

Answer 1

I suggest you derive the formula to get the present appraised value.

Let P = the value 10 years ago.
i = the interest rate of 8%
Given: apprasied value after 10 years is $3500

After year 1: the appraised value will be
P+Pi =P(1+i)
After year 2: the appraised value will be
P(1+i)+P(1+i)i= P(1+i)(1+i)
= P(1+i)^2
After year 3: the appraised value will be
P(1+i)^2+P(1+i)^2i=P(1+i)^2(1+i)
=P(1+i)^3
Let's skip the rest of the steps. Do you agree that based on the above

After year 10: the appraised value will be P(1+i)^10?

So now write this equation by substituting the given
figures:

P(1+8/100)^10=3500

Now solve for P:

P=3500/(1+8/100)^10
P=3500/2.1589
P=$1621.20

Answer 2

You have to work the question backwards. Since you know that the ring went up in value by 8% each year, that would mean that the ring would be worth 92% each year you go backwards.
Since this is over a 10 year period you would do the following:
.92^10 times 3500
This will get you the value of the ring 10 years ago.

Hope this helps. Good Luck.

Answer 3

Let X be the value of the ring 10 years ago

so X + 8% is the value of the ring 9 years ago
if x+8%=w

so w+8% is the value of the ring 8 years ago
if w+8%=v

so v+8% is the value of the ring 7 years ago
if v+8%=u

so u+8% is the value of the ring 6 years ago
if u+8%=t

so t+8% is the value of the ring 5 years ago
if t+8%=s

so s+8% is the value of the ring 4 years ago
if s+8%=r

so r+8% is the value of the ring 3 years ago
if r+8%=q

so q+8% is the value of the ring 2 years ago
if q+8%=p

so p+8% is the value of the ring 1 year ago

I hope this helps :)

Answer 4

80%+100%=$3500

100%=($3500 X 100%)/180%= Ans.

Hope this helps.

Answer 5

$700?

Answer 6

$3500=P(1.08)^10=P*2.1589
P=$3500/2.1589=$1621.18

Answer 7

3500/(1.08^10)=1621.18