Question

Laura borrows $5,000 at 10.5% compound. How much does she owe after 4 months?

Answer 1

A. Laura owes $5,177.31 at 10.5% p.a. after 4 months.

Explanation:

Although the question does not state the period over which the 10.5% rate applies, it's reasonable to assume 1 year - normally written `10.5% p.a.` (Per annum).

With that assumption, the rate per month `=r/12` so the compound interest fomula compounded monthly reduces to:

`A=P(1+r/12)^t`

Where: `P=$5,000`, `r=10.5%` and `t = 4` months
(In this example)

Hence: `A= 5000(1+10.5/(100*12))^4`

`= 5000(1+0.00875)^4`

`= 5000xx1.0352 = 5177.31` (to 2 decimals)

Laura therefore owes `$5,177.31` after 4 months.