Question

An elite private college receives large donations from successful alumni. The account that holds these donations now has $955 million.
How much would the account earn in 1 year of simple interest at a rate of 2.33%? Round to the nearest dollar.

Answer
$22,251,500

How much would the account earn in 1 year at 2.33% if the interest was compounded daily? Round to the nearest dollar.

Answer
$22,512,028

How much more interest is earned by compounding daily as compared to simple interest?

Answer
$260,528

If the money is used to pay full scholarships, and the price of tuition is $61,000 per year, how many more students each year can receive full 4-year scholarships if the interest were compounded daily rather than using simple interest?

Answer
One, since each 4-year (full) scholarship is worth $244,000.

Answer 1

1. The private college's tuition account can earn $22,251,500 in simple interest at 2.33% in one year.

2. The account would earn $22,512,028 in one year at 2.33% interest compounded daily.

3. The difference between daily compound interest and simple interest is $260,528.

4. If the money is used to pay full scholarships, and the tuition price is $61,000 per year, 4 more students can receive full 4-year scholarships with daily compounding instead of simple interest.

What is the difference between simple interest and compound interest?

Compound interest adds the earned interest to the principal and periodically compounds the new total, unlike simple interest.

Data and Calculations:

1) Simple Interest:

Principal = $955 million

Period = 1 year

Interest rate = 2.33%

Simple Interest = $22,251,500 ($955,000,000 x 2.33% x 1)

2) N (# of periods) = 365 days

I/Y (Interest per year) = 2.33%

PV (Present Value) = $955,000,000

PMT (Periodic Payment) = $0

Results:

FV = $977,512,028.18

Total Daily Compound Interest = $22,512,028.18

3) The difference between daily compound interest and simple interest is $260,528 ($22,512,028 - $22,251,500).

4) Price of tuition per year = $61,000

Additional earnings from compounding interest = $260,528

Additional students to sponsor for tuition each year = 4.27 ($260,528/$61,000).

Thus, compound interest earns more for the investor than simple interest.

Learn more about simple and compound interests at brainly.com/question/3402162

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