Answer to Question #121313 in Algebra for Neka

Question

An amount was invested at
r%
per quarter. What value of
r
will ensure that accumulated
amount at the end of one year is 1.5 times more than amount invested?

Answer 1

Solution:

SUM = X * (1 + r*d/y)ⁿ - formula for calculating the final amount on the account

where X - an amount that was invested,

r - an year interest rate in fraction form (%/100),

d - a period of payment in days,

y=365 - a number of days in the year,

n - a number of payments overall.

or for quarterly accruals:

SUM = X * (1 + r/4)ⁿ

By the end of the year there will be 4 payments.

An amount at the end of one year is 1.5 times more than amount invested, i.e. SUM=1.5*X:

1.5*X=X*(1+r/4)⁴

1.5=(1+r/4)⁴

$\frac{r}{4}+1=\sqrt[4]{1.5}$ - we consider only positive and rational roots of the equation

$r=4\cdot(\sqrt[4]{1.5}-1)\approx0.4267$ or 42.67%

Answer: r=42.67%