Interest Calculation for PA Exam - Model Paper

1. In how many years will a sum double itself at 7.5% simple interest?


Answer 
x*1.075^y=2x
y=9.58436 years

2.  a certain sum of money doubles itself at simple interest in 8 years. in how many years will it be three times at the same rate?
Answer 
principal =x
Interest =x 
x= x*8*r/100
r=100/8
--------------= 
2x= x*n*100/8 *1/100
2=100n/800 
1600=100n
n= 16 years 

3. At what rate percent compound interest does a sum of money become 2.25 times of itself in 2 years?

Answer 
A%28t%29+=+P%281%2Br%2Fn%29%5E%28nt%29
A/P = 2.25, n = 1
2.25 = (1+r)^2     (Tossing out the negative solution for unit measure) 
1.5 = (1+r)
 .5 = r

4. At what rate of interest will a sum of money amount to Rs.5310 in 2 years and Rs.6120 in 4 years?
Answer 
Interest formula:
A = P(1+r)^t

Let P = initial sum of money
and r = rate of interest
then from "Rs.5310 in 2 years" we get
5310 = P(1+r)^2 (equation 1)

and from "Rs.6120 in 4 years" we get
6120 = P(1+r)^4 (equation 2)

solve equation 1 for P:
5310 = P(1+r)^2
5310/(1+r)^2 = P

substitute above into equation 2 and solve for r:
6120 = P(1+r)^4
6120 = 5310/(1+r)^2*(1+r)^4
6120/5310 = (1+r)^2
6120/5310 = (1+r)^2
1.1525423729 = (1+r)^2
1.0736 = 1+r
.0736 = r
or
7.4% = r

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