# math

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john has a loan but doesn't begin to repay his loan for 11 months, at a rate of \$500 every month of four month. the interest rate is 8% compounded monthly determin the size of the loan using the following 2 steps

1. calculate the present value, pv1 of annuity payment at the end of the period of deferral

2. calculate the present value, pv2 of the payment at the beginning of the period of deferral

• math -

Make a time-line graph, marking months beginning at 0 (now), 1, 2, 3, ...
The way I interpret your question, the first payment will be at month 11 , then payments at 12, 13 and 14

Since the formula for an ordinary annuity assumes the first payment at the end of the first interest period, we would be finding PV1 at month 10
PV1 = 500(1 - 1.006666...^-4)/.0066666..
= 1967.106

2. now we have to "move back" this amount to the present time (now or time spot of 0)
PV2 = 1967.106(1.0066666...)^-10
= 1915.51

If the first payment is at month 12, make the appropriate changes.

• math -

an ordinary annuity starting today with eight annual payments of \$900