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Jeramiah invests his savings of $120,000 by dividing it between two in
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02 Apr 2021, 06:30
02 Apr 2021, 06:30
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Jeramiah invests his savings of $120,000 by dividing it between two interest-earning accounts. He puts 3/4 of his savings in an account that earns lower interest and 1/4 of his savings in an account that earns higher interest. He has no other accounts that earn interest and he makes $3,636 in interest by the end of the year. If one account earns 2 percent annual interest, and both accounts are compounded semiannually, what percent interest does the other account earn?
A. 3
B. 4
C. 5
D. 6
E. 7
A. 3
B. 4
C. 5
D. 6
E. 7
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Jeramiah invests his savings of $120,000 by dividing it between two in
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02 Apr 2021, 08:24
02 Apr 2021, 08:24
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GeminiHeat wrote:
Jeramiah invests his savings of $120,000 by dividing it between two interest-earning accounts. He puts 3/4 of his savings in an account that earns lower interest and 1/4 of his savings in an account that earns higher interest. He has no other accounts that earn interest and he makes $3,636 in interest by the end of the year. If one account earns 2 percent annual interest, and both accounts are compounded semiannually, what percent interest does the other account earn?
A. 3
B. 4
C. 5
D. 6
E. 7
A. 3
B. 4
C. 5
D. 6
E. 7
\(C.I = P(1 + \frac{r}{100n})^{nt} - P\)
Don't worry we will not be using this formula!
Let us solve this using S.I
\($120,000\) is divided into two Principals of \($90,000\) (with lower rate of interest) and \($30,000\) (with higher rate of interest)
Notice, the option choices are all greater than \(2\)%
This means, \($90,000\) was invested at an interest rate of \(2\)%
So, S.I \(= \frac{(90,000)(2)(1)}{100} = $1800\)
Now, \($30,000\) must give us a return of \(3636- 1800 = $1826\) at \(r\)% rate of interest in a year
i.e. \(1836 = \frac{(30,000)(r)(1)}{100}\)
\(r = 6.12\)%
Hence, option D
Re: Jeramiah invests his savings of $120,000 by dividing it between two in
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04 Jan 2024, 08:55
04 Jan 2024, 08:55
1
how semi compounding works for yearly , P= 100 and interest rate is 10% then for 6 month 5% will be applied thus interest= 5 so
amount after 6 month is 105 and for next 6 month 5% will applied on 105 thus amount =110.25
Two amount 90000 & 30000
for 90000 , total interest rate 2% thus interest for 6 months is 1% thus interest=900
for next 6 month 1% interest thus 1% of 900 = 9 , thus interest=909
now total interest after year = 900+909=1809
Remaining amount = 3636-1809=1827
for 30000 let say x% interest , now solve like above by taking values from option , lets take 6
for 1st 6 months , interest will be 3% = 3% of 30000= 900
for 2nd 6 months ,interest will be 3% = 3% of 900 = 27 thus interest =927
total = 900+927=1827 it matches thus answer is D
amount after 6 month is 105 and for next 6 month 5% will applied on 105 thus amount =110.25
Two amount 90000 & 30000
for 90000 , total interest rate 2% thus interest for 6 months is 1% thus interest=900
for next 6 month 1% interest thus 1% of 900 = 9 , thus interest=909
now total interest after year = 900+909=1809
Remaining amount = 3636-1809=1827
for 30000 let say x% interest , now solve like above by taking values from option , lets take 6
for 1st 6 months , interest will be 3% = 3% of 30000= 900
for 2nd 6 months ,interest will be 3% = 3% of 900 = 27 thus interest =927
total = 900+927=1827 it matches thus answer is D
