1. Compound Interest CI = 210, Principal P = 1000, Rate R = 10, find T (Interest Compounded Annually)
Solution:
Compound Interest `CI=210`
Principal `P=1000`
Rate of interest `R=10%`
Find `T,` (Interest Compounded Annually)
`A=P+I`
`:.A=1000+210`
`:.A=1210`
We know that
`A=P*(1+R/(100n))^(nT)`
`:.A/P=(1+R/(100n))^(nT)`
Taking `ln` both the sides
`:.ln(A/P)=nT*ln(1+R/(100n))`
`:.T=(ln(A/P))/(n*ln(1+R/(100*n)))`
`:.T=(ln(1210/1000))/(1*ln(1+10/(100xx1)))`
`:.T=(ln(1.21))/(ln(1+0.1))`
`:.T=(ln(1.21))/(ln(1.1))`
`:.T=(0.19062)/(0.09531)`
`:.T=2`
2. Compound Interest CI = 1050, Principal P = 5000, Rate R = 10, find T (Interest Compounded Annually)
Solution:
Compound Interest `CI=1050`
Principal `P=5000`
Rate of interest `R=10%`
Find `T,` (Interest Compounded Annually)
`A=P+I`
`:.A=5000+1050`
`:.A=6050`
We know that
`A=P*(1+R/(100n))^(nT)`
`:.A/P=(1+R/(100n))^(nT)`
Taking `ln` both the sides
`:.ln(A/P)=nT*ln(1+R/(100n))`
`:.T=(ln(A/P))/(n*ln(1+R/(100*n)))`
`:.T=(ln(6050/5000))/(1*ln(1+10/(100xx1)))`
`:.T=(ln(1.21))/(ln(1+0.1))`
`:.T=(ln(1.21))/(ln(1.1))`
`:.T=(0.19062)/(0.09531)`
`:.T=2`
3. Compound Interest CI = 3640, Principal P = 5000, Rate R = 20, find T (Interest Compounded Annually)
Solution:
Compound Interest `CI=3640`
Principal `P=5000`
Rate of interest `R=20%`
Find `T,` (Interest Compounded Annually)
`A=P+I`
`:.A=5000+3640`
`:.A=8640`
We know that
`A=P*(1+R/(100n))^(nT)`
`:.A/P=(1+R/(100n))^(nT)`
Taking `ln` both the sides
`:.ln(A/P)=nT*ln(1+R/(100n))`
`:.T=(ln(A/P))/(n*ln(1+R/(100*n)))`
`:.T=(ln(8640/5000))/(1*ln(1+20/(100xx1)))`
`:.T=(ln(1.728))/(ln(1+0.2))`
`:.T=(ln(1.728))/(ln(1.2))`
`:.T=(0.546965)/(0.182322)`
`:.T=3`
This material is intended as a summary. Use your textbook for detail explanation.
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