Liam deposits $$ 3, 500$ in a saving account that pays $7 \frac{1}{2} %$ interest, compounded quarterly.
$a$ . Find the first quarter’s interest.
$b$ . Find the first quarter’s ending balance.
$c$ . Find the second quarter’s interest.
$d$ . Find the second quarter’s ending balance.
$e$ . Find the third quarter’s interest.
$f$ . Find the third quarter’s ending balance.
$g$ . Find the fourth quarter’s interest.
$h$ . What is the balance at the end of one year?
$i$ . How much interest does the account earn in the first year?

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Solution

Evaluate:
Given,
Deposit amount= $$ 3, 500$
We know that-
$I = P r t$ where $I$ is interest amount, $P$ is the principal amount, $r$ is a rate of interest, and $t$ is the time period
Given,
$P = 3500$
$r = 7 \frac{1}{2} = \frac{15}{2} = 7.5 \Rightarrow r = 7.5 %$
Step- $1$ :
$a)$ The first quarter’s interest
$t = \frac{3}{12} = \frac{1}{4}$
$I = P r t$
$= 3500 \times \frac{7.5}{100} \times \frac{1}{4} = 65.625$
Hence the interest in the first quarter is $$ 65.625$
Step- $2$ :
$b)$ First quarter ending balance= $principalamount+intersetamount$
$= 3500 + 65.625 = 3565.625$
Hence, the ending balance in the first quarter is $$ 3565.625$
Step- $3$ :
$c)$ Second quarter's interest
$P = 3565.625$ $t = \frac{1}{4}$ $r = 7.5 %$
$I = P r t$
$= 3565.625 \times \frac{7.5}{100} \times \frac{1}{4} = 66.8555$
Hence the interest in the second quarter is $$ 66.8555$
Step-4:
$d)$ Second quarter's ending balance= $principalamount+interestamount$
$= 3565.625 + 66.855 = 3632.48$
Hence, the ending balance in the second quarter is $$ 3565.625$
Step- $5$ :
$e)$ Third quarter's interest
$P = 3632.48$ $t = \frac{1}{4}$ $r = 7.5 %$
$I = P r t$
$= 3632.48 \times \frac{7.5}{100} \times \frac{1}{4} = 68.109$
Hence the interest in the third quarter is $$ 68.109$
Step- $6$ :
$f)$ Third quarter's ending balance= $principalamount+intersetamount$
$= 3632.48 + 68.109 = 3700.589$
Hence, the ending balance in the third quarter is $$ 3700.589$
Step- $7$ :
$g)$ Fourth quarter's interest
$P = 3700.589$ $t = \frac{1}{4}$ $r = 7.5 %$
$I = P r t$
$= 3700.589 \times \frac{7.5}{100} \times \frac{1}{4} = 69.386$
Hence the interest in the fourth quarter is $$ 69.386$
$h)$ Balance after one year= $principalamount+intersetamount$
$= 3700.589 + 69.386 = 3769.975$
Hence, the ending balance after one year is $$ 3769.975$
$i)$ Interest on the account earn in the first year= ending balance after one year $-$ Deposit amount
$= 3769.975 - 3500 = 269.975$
Hence, Interest earned in one year is $$ 269.975$ .

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