Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $ 550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds?
$ 2750
$ 5500
$ 11000
$ 22000
$ 44000
unable to understand the explaination provided by the experts.
intrest problem
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- romitvsingh
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This seems like a calculation intensive problem
Let us assume his savings = 2x
He invests x amount in a bond that pays simple interest for 2 years
Let us represent r% = R
550 = x*r%*2 ------1
275 = x*R
He invests the other half in a bond that pays compound interest for 2 years at the same rate
A = x*(1+R)^2 -------2
A-x = 605 --------3
Substitute 1 in 2 and in 3
A = 275/R*(1+R)^2 -----4
A - 275/R = 605 ------5
AR = 275*(1+2R+R^2) ------6
AR - 275 = 605R ------7
Substitute the value of AR from equation 7 in equation 6
275+605R = 275*(1+2R+R^2)
Simplifying
R(5R-1) = 0
R=0 or R=1/5 or r% = 1/5. Substitute this value in equation 1
275 = x*1/5 or x = 1375. Our original savings were 2x or 2750
Let us assume his savings = 2x
He invests x amount in a bond that pays simple interest for 2 years
Let us represent r% = R
550 = x*r%*2 ------1
275 = x*R
He invests the other half in a bond that pays compound interest for 2 years at the same rate
A = x*(1+R)^2 -------2
A-x = 605 --------3
Substitute 1 in 2 and in 3
A = 275/R*(1+R)^2 -----4
A - 275/R = 605 ------5
AR = 275*(1+2R+R^2) ------6
AR - 275 = 605R ------7
Substitute the value of AR from equation 7 in equation 6
275+605R = 275*(1+2R+R^2)
Simplifying
R(5R-1) = 0
R=0 or R=1/5 or r% = 1/5. Substitute this value in equation 1
275 = x*1/5 or x = 1375. Our original savings were 2x or 2750
Previous answer post is good in fact, but lets understand concept and then we can derive formula quickly
let 2T be the total savings before invested
and R be the Interest rate
First Understand concept of simple and compound interest
Simple Interest will be levied only on the capital invested so, SI = T*R*2 (Amount * Interest * Period)
2TR = 550
TR = 275
Compound Interest will be levied on capital + interest on previous period , CI = T*R+(T+T*R)R (Only 2 Periods considered here Interest for first year+ Interest for second year)
TR+(TR+T)R = 605
TR+TR+TR*R = 605
2TR+TR*R = 605
550+275R = 605
R=55/275 = 1/5
We know that TR = 275
T= 275*5 = 1375
But we need 2T = 2750
Cheers,
svd
let 2T be the total savings before invested
and R be the Interest rate
First Understand concept of simple and compound interest
Simple Interest will be levied only on the capital invested so, SI = T*R*2 (Amount * Interest * Period)
2TR = 550
TR = 275
Compound Interest will be levied on capital + interest on previous period , CI = T*R+(T+T*R)R (Only 2 Periods considered here Interest for first year+ Interest for second year)
TR+(TR+T)R = 605
TR+TR+TR*R = 605
2TR+TR*R = 605
550+275R = 605
R=55/275 = 1/5
We know that TR = 275
T= 275*5 = 1375
But we need 2T = 2750
Cheers,
svd