I will calculate how long it would take her to pay off the loan at 4%
i = .04/12 = .003333...
n = ? months
PV = 200000
paym = 3000
200000 = 3000(1 - 1.003333..^-n)/.003333...
.2222... = 1 - 1.00333..^-n
1.00333...^-n = .7777...
take logs of both sides and follow log rules
-n log 1.003333... = log .7777...
-n = log .77777/log 1.003333 = appr -75.5
n = 75.5 months
Now repeat the calculation for 3%. It will obviously be a shorter period since the rate is lower.
Take the difference in times and that will be the monthly payments she would save.
Vanna has just financed the purchase of a home for $200 000. She agreed to repay the loan by making equal monthly blended payments of $3000 each at 4%/a, compounded monthly.
How much would Vanna have saved if she had obtained a loan 3%/a, compounded monthly?
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