There are two principals that need to be followed in comparing two scenarios:
- You cannot compare or combine cash amounts that exist at different moments in time. Adding the interest portions of various payments over the life of a loan, for example, is not useful.
- You need to compare scenarios that are as similar as possible, to isolate the effect of the particular difference between the scenarios.
In this case , let's consider three individuals; all have a $50,000 nest-egg earning 5% a year interest, and a burning desire to have a home renovation that can be paid off in various ways.
Andrew decides to take the first option: paying the $50,000 "price" by regular monthly payments over 15 years at 3% a year interest.
A loan calculator (Regular Payment version) tells Andrew that this means 180 monthly payments of $345.29
Being a forgetful person, Andrew decides to set aside approximately $43,650 of his nest-egg to fund the payments. A different type of loan calculator (Principal version) tells him that this portion of his nest-egg will, while earning 5%, be reduced to $0 if the 180 regular payments of $345.29 are taken from it on a monthly basis.
That leaves Andrew with his reno paid in full, the monthly payments provided for, and approximately $6350 in his nest-egg uncommitted.
Belinda chooses the second option, the "discounted price" route.
She cashes in $45,000 of her nest egg, pays off the contractor in full, and finds herself with with no further payments, and $5000 uncommitted in her nest-egg.
Charles decides to make 10 quarterly payments of $5,000 over two and a half years. Again, a loan calculator (Principal version) reveals that $46,720 of the nest-egg earning 5% will be reduced to $0 while funding the 10 quarterly payments. So Charles finds himself with the reno paid off, with no more payments to make, and $2380 uncommitted in the nest-egg.
So, Andrew comes off best, Belinda spends about $1350 more than Andrew and Charles brings up the rear spending almost $4,000 more than Andrew.
All these amounts are as of the date of payment of the bill.