Question

Greg obtains a loan for home renovations from a bank that charges simple interest at an annual rate of 3.6%. His loan is for $15,600 for 78 days. Assume each day is 1365of a year. Answer each part below.Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas.(a) Find the Interest that will be owed after 78 days.(b) Assuming Greg doesn't make any payments, find the amount owed after 78 days.

Answer 1

The rule of the simple interest is

`I=\text{PRT}`

P is the initial value

R is the annual rate in decimal

T is the time in years

Since the annual rate is 3.6%, then

`\begin{gathered} R=(3.6)/(100) \\ R=0.036 \end{gathered}`

Since his loan is $15,600, then

`P=15600`

Since the time is 78 days, then

`T=(78)/(365)`

Substitute them in the rule above

a)

`\begin{gathered} I=15600(0.036)((78)/(365)) \\ I=120.0131507 \end{gathered}`

Round it to the nearest cents (2 decimal places)

I = $120.01

The interest will be $120.01

b)

To find the amount owed after 78 days add I and P

`\begin{gathered} T=P+I \\ T=15600+120.01 \\ T=15720.01 \end{gathered}`

The amount owed after 78 days is $15720.01