A certain account pays 1.5 percent compound interest every 3 months.

Question

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. \((1.015)^4T\)

B. \((1.015)^{15}T\)

C. \((1.015)^{20}T\)

D. \(\frac{T}{(1.015)^{15}}\)

E. \(\frac{T}{(1.015)^{20}}\)

A.  (1.015)^4T

B.  (1.015)^{15}T

C.  (1.015)^{20}T

D.  \frac{T}{(1.015)^{15}}

E.  \frac{T}{(1.015)^{20}}

JerryAtDreamScore · Answer

Breaking Down the Info:

1.5\%  compound interest means we are multiplying the original amount by  101.5\%  every three months. After 5 years, we have 20 periods of 3-months, so the multiplying factor is  1.015^{20} .

Note that T is the resulting amount, however, so in order to find the principal we should divide by the factor above.

Answer: E

amilstein · Answer

shouldn't the interest of 1.5% compounded every three months be calculated as P(1+.015/4)^20=T?

LucienH · Answer

The interest rate provided is already the rate per compound period

findingmyself · Answer

Yes  LucienH

However the only catch is that 1.5% Interest is for every 3 months. The same has to be compounded into an annual interest rate which will be 6%. Use 6% and apply the same in the formula. It becomes

T= P(1+6/400)^20
Solving this, answer will be E

A certain account pays 1.5 percent compound interest every 3 months.

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A certain account pays 1.5 percent compound interest every 3 months.

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