Question

1.) Explain how periods and rates are calculated in compounding problems. Compare simple interest to compound interest.

2.) What is the difference between an ordinary annuity and an annuity due? If you were to save money in an annuity, which would you choose and why?

Answer 1

Ans : First part =Simple Interest vs. Compound Interest: An Overview

Interest is the cost of borrowing money, where the borrower pays a fee to the lender for the loan. The interest, typically expressed as a percentage, can be either simple or compounded. Simple interest is based on the principal amount of a loan or deposit. In contrast, compound interest is based on the principal amount and the interest that accumulates on it in every period. Simple interest is calculated only on the principal amount of a loan or deposit, so it is easier to determine than compound interest.

Example

Suppose Bob borrows $500,000 for three years from his rich uncle, who agrees to charge Bob simple interest at 5% annually. How much would Bob have to pay in interest charges every year, and what would his total interest charges be after three years?

(Assume the principal amount remains the same throughout the three years, i.e., the full loan amount is repaid after three years.) Bob would have to pay $25,000 in interest charges every year:$500,000×5%×1

or $75,000 in total interest charges after three years.

$25,000×3

Ans​ B part :The difference between an ordinary annuity and annuity due lies in when the payments occur – at the period's end for an ordinary annuity and at the period's beginning for an annuity due.

Example of an annuity due is rent. When you sign a lease for an apartment, you commit to pay rent on the first of each month. because the payments occur at a regular interval (monthly) and at the beginning of each period.

Example of Ordinary annuities are seen in retirement accounts, where you receive a fixed or variable payment every month from an insurance company, based on the value built up in the annuity account. In a fixed annuity account, your monthly payment is based on a fixed interest rate applied to the account balance at the start of payments. Variable annuity account payments are based on the investment performance of your account.

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