Problem 6-40 Calculating the Number of Payments [LO2] You’re prepared to make mo
ID: 2384335 • Letter: P
Question
Problem 6-40 Calculating the Number of Payments [LO2]
You’re prepared to make monthly payments of $200, beginning at the end of this month, into an account that pays 6.1 percent interest compounded monthly.
How many payments will you have made when your account balance reaches $11,000? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
You’re prepared to make monthly payments of $200, beginning at the end of this month, into an account that pays 6.1 percent interest compounded monthly.
Explanation / Answer
Rate of interest = 6.1% monthly compounded or r = (6.1/100)/12 = 0.00508333
Maturity Value F = 11000
Monthly payment at the end of the month P = 200
No of payments = n
The maturity value of an annuity can be calculated using the formula
F = P * [ (1+r)^n - 1]/r
Substituting the values
11000 = 200 * [ (1+0.00508333)^n - 1] / 0.00508333
11000 * 0.00508333 = 200 * [(1.00508333)^n - 1]
55.91663 = 200 * [(1.00508333)^n - 1]
(1.00508333)^n - 1 = 55.91663/200 --> (1.00508333)^n - 1 = 0.27958315
(1.00508333)^n = 0.27958315 +1 = 1.27958315
Taking logarithms on both sides
log (1.00508333)^n = log (1.27958315)
As log r^n = n log r
n log(1.00508333) = log (1.27958315) ---> n = log (1.27958315) / log (1.00508333)
Taking logarithm values using a scientific calculator
Number of periods for which contribution to be made
n = (0.1070685)/ (0.00220207) = 48.62
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