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# how to calculate compound interest

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A loan of \$3000 borrowed today is to be repaid in three equal installments due in one year, three years, and five years respectively. what is the size of equal installments if money is worth 7.2 % compounded monthly?

Guest Nov 22, 2014

#1
+17746
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To find the payment:     P  =  i·A / [1 - (1 + i)^(-N) ]

For one year:

i = interest rate, as a decimal, per period:  0.072 / 3  =  0.024

A = amount borrowed:  3000

N = number of payments:  3

P  =  (0.024)(3000) / [ 1 - (1 + 0.024)^(-3) ]   =  \$1048.38

For three years:    If it's three equal installments per year:      N = 9

P  =  (0.024)(3000) / [ 1 - (1 + 0.024)^(-9) ]   =  \$374.60

For five years:       If it's three equal installments per year:      N = 15

P  =  (0.024)(3000) / [ 1 - (1 + 0.024)^(-15) ]   =  \$240.52

geno3141  Nov 22, 2014
#1
+17746
+5

To find the payment:     P  =  i·A / [1 - (1 + i)^(-N) ]

For one year:

i = interest rate, as a decimal, per period:  0.072 / 3  =  0.024

A = amount borrowed:  3000

N = number of payments:  3

P  =  (0.024)(3000) / [ 1 - (1 + 0.024)^(-3) ]   =  \$1048.38

For three years:    If it's three equal installments per year:      N = 9

P  =  (0.024)(3000) / [ 1 - (1 + 0.024)^(-9) ]   =  \$374.60

For five years:       If it's three equal installments per year:      N = 15

P  =  (0.024)(3000) / [ 1 - (1 + 0.024)^(-15) ]   =  \$240.52

geno3141  Nov 22, 2014