1. A invested a sum of Rs. 64000 for 3 years at compound interest and received an amount 74088 Rs. on maturity. What is the rate of interest.
Sol:
2. On what principal will the compound interest for 3 years at 5% p.a. amount to 63.05 .
Sol:
5% = \(\frac{1}{{20}}\)
∴ P = 8000 × 0.05 = 400 Rs. Answer
Method(2): From table we remember that combined rate of 5% for 3 years is 15.7625%
∴ CI = \(\frac{{P \times 15.7625 \times 1}}{{100}}\)
= 400 Answer
3. Rs. 10000 is borrowed at CI at the rate of 1% for first year, 2% for second year and 3% for third year. Find the amount to be paid after 3 years.
Sol:
Method(1):
∴ total amount after 3 years
= 100000 + (1000 + 2000 + 3000) + (60 + 30 + 20 + 0.6)
= 106110.6 Answer
Method(2):
∴ CI = 6.1106% of 100000
= 6110.6
∴ Amount = 100000 + 6110.6
= 106110.6 Rs. Answer
Method(3): 1% = \(\frac{1}{{100}}\) 2% = \(\frac{1}{{50}}\) 3% = \(\frac{3}{{100}}\)
4. Find the amount of Rs. 1000 in 1 year at 5 p.a., compound interest payable half-yearly.
Sol:
Half yearly i.e. in 6-months.
∴ r = \(\frac{5}{{12}} \times 6\% = \frac{5}{2}\% \)
& term = 1×2 = 2 half-yearly
Method(1):
now find equivalent rate for 2 half-yearly term = 2.5 + 2.5 + \(\frac{{2.5 \times 2.5}}{{100}}\)
= 5.0625%
∴ CI = 1000×5.0625% = 50.625
∴ amount = 1000 + 50.625
=1050.625 Answer
Method(2):
5. Find the amount on Rs. 500000 in 1y8m at 24% p.a., compound interest being calculate in every 5 months.
Sol:-
P = 500000
r = 24% p.a.
t = 1y 8m = 20m
compounded in every 5 months
∴ r’ = \(\frac{{24}}{{12}} \times 5\) = 10%
& term = \(\frac{{20}}{5}\) = 4
Now apply tree method
∴ CI = 50000 × 4 + 5000 × 6 + 500 × 4 + 50
= 232050
∴ amount = 500000 + 232050
= 732050 Rs. Answer
Method(2): r’ = 10% = \(\frac{1}{{10}}\)
Method(3):
10% 10% 10% 10%
⟶ 10 + 10 + \(\frac{{10 \times 10}}{{100}}\) = 21%
21 + 10 + \(\frac{{21 \times 10}}{{100}}\)
= 32.1
⟶ 32.1 + 10 + \(\frac{{32.1 \times 10}}{{100}}\)
= 46.41%
∴ CI = 46.41% of 500000
= 232050
∴ A = 500000 + 232050 = 732050 Rs. Answer
6. Find the compound interest of third yera only on Rs. 10000 in 9 months at 4% p.a. interest payable quarterly.
Sol:
Interest is payable quaterly & there are 4 quarters in a year. So interest will be payable every \(\frac{{12}}{4}\) = 3 months.
P = 10000
r = 4% p.a. ⟹ r’ = \(\frac{4}{{12}}\)×3 = 1%
t = 9 months ⟹ t’ = \(\frac{9}{3}\) = 3
∴ CI of 3ʳᵈ year = 100 + 1 + 1 + \(\frac{1}{{100}}\)
= 102.01 Answer
7. Find the compound interest on Rs. 16000 in 3 months at 5% p.a., interest payable quarterly.
Sol:
P = 16000
r = 5%
t = 3 months
compounding-period = 3 months (quarterly)
∴ r’ = \(\frac{5}{{12}}\)×3 = \(\frac{5}{4}\)% = \(\frac{1}{{80}}\)%
t’ = \(\frac{3}{3}\) = 1
8. What principal will amount to Rs. 7935 in 2 years at 15% p.a. compound interest.
Sol:
15% = \(\frac{3}{{20}}\)
Method(2):
15 + 15 + \(\frac{{15 \times 15}}{{100}}\) = 32.25%
∴ CI = P × 32.25%
A = P(1 + 32.25%)
P = \(\frac{{7935}}{{1.3225}}\)
P = 6000 Answer
Method(3):
9. At what rate percent compound interest, will Rws. 256 amount to Rs. 289 in 2 years ?
Sol:
10. On what sum will the amount for 2.75 years at 10% p.a. becomes Rs. 123507.125 ?
Sol:
time = 2.75 years
r = 10% = \(\frac{1}{{10}}\)
Now CI of 3ʳᵈ year = 100 + 10 + 10 + 1 = 121
but in question whole third year is not taken only 0.75 year is taken
∴ CI for 0.75 year in third year = 121 × 0.75
= 90.75
∴ total CI of 2.75 years =
100 × 2 + 10 + 90.75
= 300.75
∴ A = P + CI
= 1000 + 300.75