at what rate percent a sum of rupees 1600 amount 1933 after 2 year if interest is compounded half yearly solve only with the help of logarithms g
Answers
Answer:
The rate percent it takes a sum of rupees 1600 to amount to rupees 1933 after 2 years, compounded half yearly is 12%
Step-by-step explanation:
The compound interest formula is as follows:
A = P ( 1 + r/n) ⁿᵇ
Where A = Amount accrued , Rs. 1933
P = Principal borrowed/lend Rs. 1600
r = Interest rate per annum ( in decimal form) , ?
n = number of times compounded per year, (half year = 2 times in
year) = 2
b = Number years the principal is compounded, 2 years = 2
Therefore, substitute these figures in your formula:
A = P ( 1 + r/n) ⁿᵇ
1933 = 1600 ( 1 + r/2)²ˣ²
1933 = 1600 ( 1 + r/2)⁴
Divide both sides by 1600
1933/1600 = 1600/1600( 1+r/2)⁴
1.208125 = (1 + r/2)⁴
Introduce logarithm at this point to solve this equation, log
log 1.208125 = log(1+r/2)⁴
log 1.208125 = 4log(1+0.5r).....Power rule
0.82112 = 4 log (1+0.5r)
Divide both sides by 4
0.02053 = log ( 1+ 0.5r)
This therefore means :
10 ^ 0.0253 = (1 + 0.5r)
1.06 = 1 + 0.5r
0.5r = 1.06 - 1
0.5 r = 0.06
r = 0.06/0.5
r = 0.12
Therefore the interest rate per annum in decimal form is 0.12
Convert this to percentage = 0.12 × 100/100%
= 12%
There rate percent therefore = 12%