/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 68 A deposit of $$\$ 5000$$ is made... [FREE SOLUTION] | 91影视

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Chapter 3: Problem 68

A deposit of $$\$ 5000$$ is made in a trust fund that pays \(7.5 \%\) interest, compounded continuously. It is specified that the balance will be given to the college from which the donor graduated after the money has earned interest for 50 years. How much will the college receive?

Short Answer

Expert verified
The college will receive approximately \$86560.34 after 50 years.

Step by step solution

01

Identify Known Variables

The initial principal amount \(P\) is $5000. The annual interest rate \(r\) is 7.5\% or in decimal form, \(0.075\). The money will be held for 50 years, so \(t = 50\).
02

Apply Continuous Compound Interest Formula

Insert \(P\), \(r\) and \(t\) in the formula \(A = Pe^{rt}\) to calculate the final amount \(A\).
03

Calculate Final Amount

\(A = \$5000 \cdot e^{0.075\cdot50} = \$5000 \cdot e^{3.75}\)
04

Simplify Calculation

Using a calculator, the final amount \( A \) will be approximately \$86560.34.

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