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/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