# Geometric Progression

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A mortagge is taken out for \$10,000 and is repaid by annual installments of \$2,000. Interest is charged on the outstanding debt at 10%, calculated annually. If the first repayment is made one year the after the mortagage is taken out, find out the number of years it takes for the mortage to be repaid.

• Geometric Progression -

10000 = 2000(1 - 1.1^-n)/.1
5 = (1 - 1.1^-n)/.1
.5 = 1 - 1.1^-n
1.1^-n = .5
log both sides
-n log 1.1 = log .5
-n = log .5/log 1.1 = -7.27
n = 7.27
or appr 7 and 1/4 years

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