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An insurance company client deposits $1,000,000 for an annuity payment of $6000 per month. The annual...

An insurance company client deposits $1,000,000 for an annuity payment of $6000 per month. The annual contracted discount rate of 4% is compounded monthly. The insurance company fee is 2% of the deposit.

How many months does the annuity last?

What is the formula for n?

Solutions

Expert Solution

Given,

Amount of deposit= $1,000,000

Insurance company fee= 2% of deposit

Therefore, net amount (PV) = $1,000,000*(1-2%)= $980,000

Number of payments= 236. 26 calculated as follows:

Formula for ‘n’ is as follows:

n=-{ln(1-[PV*i]/PMT)/ln(1+i)}

Where n= Number of payments, PV= Present balance, PMT= periodical payments and i= Interest rate per period.   ln is the natural logarithm with base 'e'

jeff jeffy answered 2 years ago
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