Question

John requires $\$ 3000$ in 6 months to pay off a loan that has no prepayment privileges. If he has the $\$ 3000$ now, how much of it should he save in an account paying $3 \%$ compounded monthly so that in 6 months he will have exactly $\$ 3000 ?$

Name: Problem 46, Chapter 5: Precalculus
Uploaded: 2020-07-07T10:38:21-08:00
Duration: 2 min 16 s
Channel: Neel Faucher
Description: John requires 3000 in 6 months to pay off a loan that has no prepayment privileges. If he has the 3000 now, how much of it should he save in an account paying 3 % compounded monthly so that in 6 months he will have exactly 3000 ?

   John requires $\$ 3000$ in 6 months to pay off a loan that has no prepayment privileges. If he has the $\$ 3000$ now, how much of it should he save in an account paying $3 \%$ compounded monthly so that in 6 months he will have exactly $\$ 3000 ?$

Precalculus

Michael Sullivan 9th Edition

Chapter 5, Problem 46

Instant Answer

Solved by Expert Neel Faucher

07/07/2020

Step 1

The rate of interest (R) is 3%, the number of compounds per year (n) is 12 since it's compounded monthly, the amount (A) is $3000, and the time (t) is 6 months or 0.5 years. Show more…

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John requires $\$ 3000$ in 6 months to pay off a loan that has no prepayment privileges. If he has the $\$ 3000$ now, how much of it should he save in an account paying $3 \%$ compounded monthly so that in 6 months he will have exactly $\$ 3000 ?$

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Key Concepts

Time Value of Money

This concept states that a sum of money available today is worth more than the same sum in the future due to its potential earning capacity. It is fundamental when comparing cash flows that occur at different times.

Present Value

Present value is the current worth of a future sum of money given a specific rate of return. It involves discounting the future amount back to the present using an appropriate interest rate and compounding frequency.

Compound Interest

Compound interest is the process where interest is calculated on the initial principal and also on the accumulated interest from previous periods. This results in exponential growth over time as interest is earned on interest.

Periodic Compounding

Periodic compounding refers to the calculation of interest on a principal amount at regular intervals, such as monthly or annually. This concept is crucial when determining the effective growth of an investment or savings over time.

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