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A certain account pays 1.5 percent compound interest every

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A certain account pays 1.5 percent compound interest every  [#permalink]

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New post 29 Jul 2013, 09:09
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A certain account pays 1.5 percent compound interest every 3 months. A person invested an initial amount and did not invest any more money in the account after that. If after exactly 5 years, the amount of money in the account was T dollars, which of the following is an expression for the original number of dollars invested in the account?

a) [(1.015)^4]T
b) [(1.015)^15]T
c) [(1.015)^20]T
d) [T/{(1.015)^15}]
e) [T/{(1.015)^20}]
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Re: A certain account pays 1.5 percent compound interest every  [#permalink]

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New post 29 Jul 2013, 09:14
5 years = 60 months, so his compound interest will be paid \(\frac{60}{3}=20\) times in total.

I=initial amount, T = final amount.

\(I(1+0.015)^{20}=T\) or \(I=\frac{T}{(1+0.015)^{20}}\).

E
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Re: A certain account pays 1.5 percent compound interest every  [#permalink]

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New post 29 Jul 2013, 13:08
Zarrolou wrote:
5 years = 60 months, so his compound interest will be paid \(\frac{60}{3}=20\) times in total.

I=initial amount, T = final amount.

\(I(1+0.015)^{20}=T\) or \(I=\frac{T}{(1+0.015)^{20}}\).

E


But, here the interest is not paid annually but quarterly. So,shouldn't we divide the rate also by 20.
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Re: A certain account pays 1.5 percent compound interest every  [#permalink]

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New post 30 Jul 2013, 11:11
Gian wrote:
Zarrolou wrote:
5 years = 60 months, so his compound interest will be paid \(\frac{60}{3}=20\) times in total.

I=initial amount, T = final amount.

\(I(1+0.015)^{20}=T\) or \(I=\frac{T}{(1+0.015)^{20}}\).

E


But, here the interest is not paid annually but quarterly. So,shouldn't we divide the rate also by 20.



@zarrolou/experts

Could anyone throw some light on the above confusion.
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Re: A certain account pays 1.5 percent compound interest every  [#permalink]

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New post 30 Jul 2013, 14:24
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Gian wrote:
Gian wrote:
Zarrolou wrote:
5 years = 60 months, so his compound interest will be paid \(\frac{60}{3}=20\) times in total.

I=initial amount, T = final amount.

\(I(1+0.015)^{20}=T\) or \(I=\frac{T}{(1+0.015)^{20}}\).

E


But, here the interest is not paid annually but quarterly. So,shouldn't we divide the rate also by 20.



@zarrolou/experts

Could anyone throw some light on the above confusion.


Hi Gian

The original formula of "annual compound interest rate" is:
t = number of years
i = annual interest rate
T = future value (FV)
P = Present value (PV)

After t year:
FV = PV[1 + i]^t

If interest rate is quarterly, then
new interest rate/period = i/4
new number of periods = t*4

The new formula is:
FV = PV[1 + i/4]^4t

Apply to this question:
T = PV[1 + 0.015]^20
Because i/4 = 1.5%
number of periods = 4*5 = 20

So, PV = T/[1.015]^20
--Or--
PV = T*[1.015]^-20

Hope it helps
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Re: A certain account pays 1.5 percent compound interest every  [#permalink]

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New post 30 Jul 2013, 14:39
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Gian wrote:
But, here the interest is not paid annually but quarterly. So,shouldn't we divide the rate also by 20.


Hi Gian.

1.5% is quarterly interest rate = interest rate/period
20 = number of quarters (4 quarters x 5 years) = number of period

After 1 quarter ==> FV = PV*(1 + 1.5%)
After 2 quarters ==> FV = [PV*(1 + 1.5%)]*(1 +1.5%) = PV*(1 +1.5%)^2
....
After 20 quarters ==> FV = PV*(1 +1.5%)^20

The original formula of compound interest rate is:
FV = PV*(1 + interest rate per period)^number of periods
Thus, we do not divide the rate by 20 because 1.5% is interest per period and 20 is the number of periods.

Hope it's clear.
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Compound Interest Question  [#permalink]

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New post 08 Feb 2018, 12:05
This question is from Kaplan practice book, and I think the answer is wrong. If an account pays 1.5% compound interest every 3 months, it is quarterly which means the interest rate should be divided by 4 (1+0.015/4). The book says that the answer is E. Is this answer flawed or am I wrong?


A certain account pays 1.5 percent compound interest every 3 months. A person
invested an initial amount and did not invest any more money in the account
after that. If after exactly 5 years, the amount of money in the account was T
dollars, which of the following is an expression for the original number of dollars
invested in the account?
= T(1.015)^4
= T(1.015)^15
= T(1.015)^20
= T/(1.015)^15
= T/(1.015)^20
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Re: A certain account pays 1.5 percent compound interest every  [#permalink]

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New post 11 Feb 2018, 20:07
rockubabe wrote:
This question is from Kaplan practice book, and I think the answer is wrong. If an account pays 1.5% compound interest every 3 months, it is quarterly which means the interest rate should be divided by 4 (1+0.015/4). The book says that the answer is E. Is this answer flawed or am I wrong?


A certain account pays 1.5 percent compound interest every 3 months. A person
invested an initial amount and did not invest any more money in the account
after that. If after exactly 5 years, the amount of money in the account was T
dollars, which of the following is an expression for the original number of dollars
invested in the account?
= T(1.015)^4
= T(1.015)^15
= T(1.015)^20
= T/(1.015)^15
= T/(1.015)^20


So I too was confused but now I understand. It says it pays 1.5% every 3 months, that is already the quarterly rate. So technically it pays 6% compounded quarterly.

6/4 = 1.5 every three months.

So that's why the answer is T/(1.015)^20

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Re: A certain account pays 1.5 percent compound interest every &nbs [#permalink] 11 Feb 2018, 20:07
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